Category: ICSE

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 4 Decimal Fractions (Decimals)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 4 Decimal Fractions (Decimals)

Decimal Fractions Exercise 4A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Convert the following into fractions in their lowest terms :
(i) 3.75
(ii) 0.5
(iii) 2.04
(iv) 0.65
(v) 2.405
(vi) 0.085
(vii) 8.025
Solution:

Question 2.
Convert into decimal fractions

Solution:

Question 3.
Write the number of decimal places in :
(i) 0.4762
(ii) 7.00349
(iii) 8235.403
(iv) 35.4
(v) 2.608
(vi) 0.000879
Solution:

Question 4.
Write the following decimals as word statements :
(i) 0.4,0.9,0.1
(ii) 1.9, 4.4, 7.5
(iii) 0.02, 0.56, 13.06
(iv) 0.005,0.207, 111.519
(v) 0.8, 0.08, 0.008, 0.0008
(vi)256.1, 10.22, 0.634
Solution:

Question 5.
Convert the given fractions into like fractions:
(i) 0.5,3.62,43.987 and 232.0037
(ii) 215.78, 33.0006, 530.3 and 0.03569
Solution:

Decimal Fractions Exercise 4B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Add:
(i) 0.5 and 0.37 (ii) 3.8 and 8.7
(iii) 0.02, 0.008 and 0.309
(iv) 0. 4136, 0. 3195 and 0.52
(v) 9.25, 3.4 and 6.666
(vi) 3.007, 0.587 and 18.341
(vii) 0.2, 0.02 and 2.0002
(viii) 6. 08, 60.8, 0.608 and 0.0608
(ix) 29.03, 0.0003, 0.3 and 7.2
(x) 3.4, 2.025, 9.36 and 3.6221
Solution:

Question 2.
Subtract the first! number from the second :
(i) 5.4, 9.8
(ii) 0.16, 4.3
(iii) 0.82, 8.6
(v) 2.237, 9.425
(vi) 41 .03, 59.46
(vii) 3.92. 26.86
(viii) 4.73, 8.5
(ix) 12.63, 36.2
(x) 0.845, 3.71
Solution:

Question 3.
Simplify :
(i) 28.796 -13.42 – 2.555
(ii) 93.354 – 62.82 – 13.045
(iii) 36 – 18.59 – 3.2
(iv) 86 + 16.95 – 3.0042
(v) 32.8 – 13 – 10.725 +3.517
(vi) 4000 – 30.51 – 753.101 – 69.43
(vii) 0.1835 + 163.2005 – 25.9 – 100
(viii) 38.00 – 30 + 200.200 – 0.230
(ix) 555.555 + 55.555 – 5.55 – 0.555
Solution:

Question 4.
Find the difference between 6.85 and 0.685.
Solution:

Question 5.
Take out the sum of 19.38 and 56.025 then subtract it from 200. 111.
Solution:

Question 6.
Add 13.95 and 1.003 ; and from the result, subtract the sum of 2.794 and 6.2.
Solution:

Question 7.
What should be added to 39.587 to give 80.375 ?
Solution:

Question 8.
What should be subtracted from 100 to give 19.29?
Solution:

Question 9.
What is the excess of 584.29 over 213.95 ?
Solution:

Question 10.
Evaluate:
(i) (5.4 – 0.8) + (2.97 -1.462)
(ii) (6.25 + 0.36) -(17.2 – 8.97)
(iii) 9.004 + (3 -2.462)
(iv) 879.4 – (87.94 – 8 .794)
Solution:

Question 11.
What is the excess of 75 over 48.29?
Solution:

Question 12.
If A = 237.98 and B = 83.47.
Find :
(i) A – B
(ii) B – A.
Solution:

Question 13.
The cost of one kg of sugar increases from ?28.47 to T32.65. Find the increase in cost.
Solution:

Decimal Fractions Exercise 4C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Multiply:
(i) 0.87 by 10
(ii) 2.948 by 100
(iii) 6.4 by 1000
(iv) 5.8 by 4
(v) 16.32 by 28
(vi) 5. 037 by 8
(vi) 4.6 by 2.1
(viii) 0.568 by 6.4
Solution:

Question 2.
Multiply each number by 10, 100, 1000 :
(i) 0.5
(ii) 0.112
(iii) 4.8
(iv) 0.0359
(v) 16.27
(vi) 234.8
Solution:

Question 3.
Evaluate:
(i) 5.897 x 2.3
(ii) 0.894 x 87
(iii) 0.01 x 0.001
(iv) 0.84 x 2.2 x 4
(v) 4.75 x 0.08 x 3
(vi) 2.4 x 3.5 x 4.8
(vii) 0.8 x 1.2 x 0.25
(viii) 0.3 x 0.03 x 0.003
(ix) 12.003 x (0.2)⁵
Solution:

Question 4.
Divide :
(i) 54.9 by 10
(ii) 7.8 by 100
(iii) 324.76 by 1000
(iv) 12.8 by 4
(v) 27.918 by 9
(vi) 4.672 by 8
(vii) 4.32 by 1.2
(viii) 7.644 by 1.4
(ix) 4.8432 by 0.08
Solution:

Question 5.
Divide each of the given numbers by 10, 100, 1000 and 10000
(i) 2.1
(ii) 8.64
(iii) 5-01
(iv) 0.0906
(v) 0.125
(vi) 111.11
(vii) 0.848 x 3
(viii)4.906 x (0.2) ²
(ix) (1.2)² x(0.9)²
Solution:

Question 6.
Evaluate :
(i) 9.75 + 5
(ii) 4.4064 + 4
(iii) 27.69 + 30
(iv) 19.25 + 25
(v) 20.64+ 16
(vi) 3.204 + 9
(vii) 0.125 + 25
(viii) 0.14616 + 72
(ix) 0.6227+ 1300
(x) 257.894+ 0-169
(xi) 6.3 + (0.3)²
Solution:

Question 7.
Evaluate:
(i) 4.3 x 0.52 x 0.3
(ii) 3.2 x 2.5 x 0.7
(iii) 0.8 x 1.5 x 0.6
(iv) 0.3 x 0.3 x 0.3
(v) 1.2 x 1.2 x 0.4
(vi) 0.4 x 0.04 x 0.004
(vii) 0.5 x 0.6 x 0.7
(Viii) 0.5 x 0.06 x 0.007
Solution:

Question 8.
Evaluate:
(i) (0.9)²
(ii) (0.6)² x 0.5
(iii) 0.3 x (0.5)²
(iv) (0.4)³
(v) (0.2)³ x 5
(vi) (0.2)³ x 0.05
Solution:

 Question 9.
Find the cost of 36.75 kg wheat at the rate of ₹12.80 per kg.
Solution:

Question 10.
The cost of a pen is ₹56.15. Find the cost of 16 such pens.
Solution:

Question 11.
Evaluate:
(i) 0.0072 ÷ 0.06
(ii) 0.621 ÷ 0.3
(iii) 0.0532 ÷ 0.005
(iv) 0.01162 ÷ 0.14
(v) (7.5 x 40.4) ÷ 25
(vi) 2.1 ÷ (0.1 x 0.1)
Solution:

Question 12.
Fifteen indentical articles weigh 31.50 kg. Find the weight of each article.
Solution:

Question 13.
The product of two numbers is 211.2. If one of these two numbers is 16.5, find the other number.
Solution:

Question 14.
One dozen identical articles cost ₹45.96. Find the cost of each article.
Solution:

Decimal Fractions Exercise 4D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find whether the given division forms a terminating decimal or a non-terminating decimal:
(i) 3 ÷ 8
(ii) 8 ÷ 3
(iii) 6÷ 5
(iv) 5 ÷ 6
(v) 12.5 ÷ 4
(vi) 23 ÷ 0.7
(vii) 42 ÷ 9
(viii) 0.56÷ 0.11
Solution:

Question 2.
Express as recurring decimals :

Solution:

Question 3.
Convert into vulgar fraction :
(i) 0.\(\bar { 3 }\)
(ii) 0.\(\bar { 8 }\)
(iii) 4.\(\bar { 4 }\)
(iv) 23.\(\bar { 7 }\)
Solution:

Question 4.
Convert into vulgar fraction :
(i) 0.\(\bar { 35 }\)
(ii) 2.\(\bar { 23 }\)
(iii) 1.\(\bar { 28 }\)
(iv) 5.\(\bar { 234 }\)
Solution:

Question 5.
Convert into vulgar fraction :
(i) 0 0.3\(\bar { 7 }\)
(ii) 0.2\(\bar { 45 }\)
(iii) 0.68\(\bar { 5 }\)
(iv) 0.4\(\bar { 42 }\)
Solution:

Decimal Fractions Exercise 4E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Round off:
(i) 0 .07, 0.112, 3.59, 9.489 to the nearest tenths.
(ii) 0.627, 100.479, 0 065 and 0.024 to the nearest hundredths.
(iii) 4.83,0.86,451 .943 and 9.08 to the nearest whole number.
Solution:

Question 2.
Simplify, and write your answers correct to the nearest hundredths :
(i) 18 .35 x 1.2
(ii) 62.89 x 0.02
Solution:

Question 3.
Write the number of significant figures (digits) in:
(i) 35.06
(ii) 0.35
(iii) 7.0068
(iv) 19 .0
(v) 0.0062
(vi) 0 4.2 x 0.6
(vii) 0.08 x 25
(viii) 3.6 ÷ 0.12 .
Solution:

Question 4.
Write :
(i) 35.869,0 008426,4.952 and 382.7, correct lo three significant figures.
(ii) 60.974. 2.8753, 0.001789 and 400.04, correct to four significant figures.
(iii) 14.29462, 19.2, 46356.82 and 69, correct to five significant figures.
Solution:

Decimal Fractions Exercise 4F – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The weight of an object is 3 .06 kg. Find the total weight of 48 similar objects.
Solution:

Question 2.
Find die cost of 17.5 m cloth at the rate of Rs. 112.50 per metre.
Solution:

Question 3.
One kilogramme of oil costs Rs. 73.40. Find the cost of 9.75 kilogramme of the oil.
Solution:

Question 4.
Total weight of 8 identical objects is 51.2 kg. Find the weight of each object.
Solution:

Question 5.
18.5 m of cloth costs Rs. 666. Find the cost of 3.8 m cloth.
Solution:

Question 6.
Find die value of:
(i) 0.5 of Rs. 7.60 + 1.62 of Rs. 30
(ii) 2.3 of 7.3 kg + 0.9 of 0.48 kg
(iii) 6.25 of 8.4 – 4.7 of 3.24
(iv) 0.98 of 235 – 0 .09 of 3.2
Solution:

Question 7.
Evaluate:
(i) 5.6 – 1 .5 of 3.4
(ii) 4.8 ÷ 0.04 of 5
(iii) 0.72 of 80 + 0.2
(iv) 0.72 ÷ 80 of 0.2
(v) 6.45 + (3.9 – 1.75)
(vi) 0.12 of(0.104 – 0.02)+ 0.36 x 0.5
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 1 Rational Numbers

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 1 Rational Numbers

Rational Numbers Exercise 1A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Add, each pair of rational numbers, given below, and show that their addition (sum) is also a rational number:

Solution:

Question 2.
Evaluate:

Solution:

Question 3.
Evaluate:

Solution:

Question 4.
For each pair of rational numbers, verify commutative property of addition of rational numbers:

Solution:

Question 5.
For each set of rational numbers, given below, verify the associative property of addition of rational numbers:

Solution:

Question 6.
Write the additive inverse (negative) of:

Solution:

Question 7.
Fill in the blanks:

Solution:

Question 8.
State, true or false:

Solution:

Rational Numbers Exercise 1B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Subtract:

Solution:

Question 3.
The sum of two rational numbers is \(\frac { 9 }{ 20 }\). If one of them is \(\frac { 2 }{ 5 }\), find the other.
Solution:

Question 4.
The sum of the two rational numbers is \(\frac { -2 }{ 3 }\). If one of them is \(\frac { -8 }{ 5 }\), find the other.
Solution:

Question 5.
The sum of the two rational numbers is -6. If one of them is \(\frac { -8 }{ 5 }\), find the other.
Solution:

Question 6.
Which rational number should be added to \(\frac { -7 }{ 8 }\) to get \(\frac { 5 }{ 9 }\) ?
Solution:

Question 7.
Which rational number should be added to \(\frac { -5 }{ 9 }\) to get \(\frac { -2 }{ 3 }\) ?
Solution:

Question 8.
Which rational number should be subtracted from \(\frac { -5 }{ 6 }\) to get \(\frac { 4 }{ 9 }\) ?
Solution:

Question 9.
(i) What should be subtracted from -2 to get \(\frac { 3 }{ 8 }\)
(ii) What should be added to -2 to get \(\frac { 3 }{ 8 }\)
Solution:

Question 10.
Evaluate:

Solution:

Rational Numbers Exercise 1C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Multiply:

Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Multiply each rational number, given below, by one (1):

Solution:

Question 5.
For each pair of rational numbers, given below, verify that the multiplication is commutative:

Solution:

Question 6.
Write the reciprocal (multiplicative inverse) of each rational number, given below :

Solution:

Question 7.
Find the reciprocal (multiplicative inverse) of:

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
Name the multiplication property of rational numbers shown below :

Solution:

Question 11.
Fill in the blanks:
(i) The product of two positive rational numbers is always ……………
(ii) The product of two negative rational numbers is always ……………
(iii) If two rational numbers have opposite signs then their product is always …………..
(iv) The reciprocal of a positive rational number is ………. and the reciprocal of a negative rational number is ……………
(v) Rational number 0 has ………….. reciprocal.
(vi) The product of a rational number and its reciprocal is ………..
(vii) The numbers ……….. and ……….. are their own reciprocals.
(viii) If m is reciprocal of n, then the reciprocal of n is ………….
Solution:

Rational Numbers Exercise 1D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Divide:

Solution:

Question 3.
The product of two rational numbers is -2. If one of them is \(\frac { 4 }{ 7 }\), find the other.
Solution:

Question 4.
The product of two numbers is \(\frac { -4 }{ 9 }\). If one of them is \(\frac { -2 }{ 27 }\), find the other.
Solution:

Question 5.
m and n are two rational numbers such that

Solution:

Question 6.
By what number must \(\frac { -3 }{ 4 }\) be multiplied so that the product is \(\frac { -9 }{ 16 }\) ?
Solution:

Question 7.
By what number should \(\frac { -8 }{ 13 }\) be multiplied to get 16?
Solution:

Question 8.
If 3\(\frac { 1 }{ 2 }\) litres of milk costs ₹49, find the cost of one litre of milk?
Solution:

Question 9.
Cost of 3\(\frac { 2 }{ 5 }\) metre of cloth is ₹88\(\frac { 1 }{ 2 }\). What is the cost of 1 metre of cloth?
Solution:

Question 10.
Divide the sum of \(\frac { 3 }{ 7 }\) and \(\frac { -5 }{ 14 }\) by \(\frac { -1 }{ 2 }\).
Solution:

Question 11.

Solution:

Question 12.
The product of two rational numbers is -5. If one of these numbers is \(\frac { -7 }{ 15 }\), find the other.
Solution:

Question 13.
Divide the sum of \(\frac{5}{8}\) and \(\frac{-11}{12}\) by the difference of \(\frac{3}{7}\) and \(\frac{5}{14}\)
Solution:

Rational Numbers Exercise 1E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.
Insert one rational number between (0 7 and 8 (ii) 3.5 and 5
(i) 2 and 3.2
(ii) 3.5 and 5
(iii) 2 and 3.2
(iv) 4.2 and 3.6
(v) \(\frac { 1 }{ 2 }\) and 2
Solution:

Question 4.
Insert two rational numbers between
(i) 6 and 7
(ii) 4.8 and 6
(iii) 2.7 and 6.3
Solution:

Question 5.
Insert three rational numbers between
(i) 3 and 4
(ii) 10 and 12
Solution:

Question 6.
Insert five rational numbers between \(\frac { 3 }{ 5 }\) and \(\frac { 2 }{ 5 }\)
Solution:

Question 7.
Insert six rational numbers between \(\frac { 5 }{ 6 }\) and \(\frac { 8 }{ 9 }\)
Solution:

Question 8.
Insert seven rational numbers between 2 and 3.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Fundamental Concepts Exercise 18A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 8 and x is equal to y.
(ii) x decreased by 5 is equal to y.
(iii) The sum of 2 and x is greater than y.
(iv) The sum of x and y is less than 24.
(v) 15 multiplied by m gives 3n.
(vi) Product of 8 and y is equal to 3x.
(vii) 30 divided by b is equal to p.
(viii) z decreased by 3x is equal to y.
(ix) 12 times of x is equal to 5z.
(x) 12 times of x is greater than 5z.
(xi) 12 times of x is less than 5z.
(xii) 3z subtracted from 45 is equal to y.
(xiii) 8x divided by y is equal to 2z.
(xiv) 7y subtracted from 5x gives 8z.
(xv) 7y decreased by 5x gives 8z.
Solution:

Question 2.
For each of the following algebraic expressions, write a suitable statement in words:
(i) 3x + 8=15
(ii) 7 – y > x
(iii) 2y – x < 12
(iv) 5 ÷ z = 5
(v) a + 2b > 18
(vi) 2x – 3y= 16
(vii) 3a – 4b > 14
(viii) b + 7a < 21
(ix) (16 + 2a) – x > 25
(x) (3x + 12) – y < 3a
Solution:

Fundamental Concepts Exercise 18B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Separate the constants and the variables from each of the following:

Solution:

Question 2.
Group the like terms together :

Solution:

Question 3.
State whether true or false :
(i) 16 is a constant and y is a variable but 16y is variable.
(ii) 5x has two terms 5 and x.
(iii) The expression 5 + x has two terms 5 and x
(iv) The expression 2x² + x is a trinomial.
(v) ax² + bx + c is a trinomial.
(vi) 8 x ab is a binomial.
(vii) 8 + ab is a binomial.
(viii) x³ – 5xy + 6x + 7 is a polynomial.
(ix) x³ – 5xy + 6x + 7 is a multinomial.
(x) The coefficient of x in 5x is 5x.
(xi) The coefficient of ab in – ab is – 1.
(xii) The coefficient of y in – 3xy is – 3
Solution:

Question 4.
State the number of terms in each of the following expressions :

Solution:

Question 5.
State whether true or false:
(i) xy and – yx are like terms.
(ii) x²y and – y²x are like terms.
(iii) a and – a are like terms.
(iv) – ba and 2ab are unlike terms.
(v) 5 and 5x are like terms.
(vi) 3xy and 4xyz are unlike terms.
Solution:

Question 6.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.

Solution:

Question 7.
Write down the coefficient of x in the following monomial :

Solution:

Question 8.
Write the coefficient of :

Solution:

Question 9.
State the numeral coefficient of the following monomials :

(vii) – 7x ÷ y
(viii) – 3x ÷ (2y)
Solution:

Question 10.
Write the degree of each of the following polynomials :

Solution:

Fundamental Concepts Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 3x and 4y is 8.
(ii) 5x decreased by 7 gives y.
(iii) 31 added to 4x gives 6x.
(iv) 3x subtracted from 89 gives 44.
Solution:

Question 2.
Group the like terms :

Solution:

Question 3.
Write the number of terms in each of the following polynomials :

Solution:

Question 4.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial:
(i) x + y
(ii) 5x – 4y
(iii) 7x² + 5x + 8
(iv) 64 + 3 ÷ 6
(v) 9 ÷ a x b
(vi) 8a ÷ b
Solution:

Question 5.
Write the coefficient of x2y in :
(i) -7x²yz
(ii) 8abx²y
(iii) – x²y
Solution:

Question 6.
Write the coefficient of :
(i) x² in – 8x²y
(ii) y in -4y
(iii) x in – xy²
Solution:

Question 7.
Write the numeral coefficient in :

Solution:

Question 8.
Write the degree of each of the following polynomials :

Solution:

Question 9.
Write each statement, given below in algebraic form :
(i) 28 more than twice of x is equal to 45.
(ii) 3y reduced by 5z is greater than 8x.
(iii) 6x divided by 13y is less than 17.
(iv) 9 multiplied by 5x is equal to 2y.
Solution:

Question 10.
State whether true or false :
(i) If 23 is a constant and x is a variable, 23 + x is constant.
(ii) If 23 is a constant and x is a variable, 23x is a variable.
(iii) If y is a variable and 57 is a constant, y – 57 is a variable.
(iv) If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x x 2y is a variable.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 11 Fundamental Concepts (Including Fundamental Operations)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 11 Fundamental Concepts (Including Fundamental Operations)

Fundamental Concepts Exercise 11A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Separate constant terms and variable terms from tile following :

Solution:

Question 2.
Constant is only 8 others are variables
(i) 2x ÷ 15
(ii) ax+ 9
(iii) 3x² × 5x
(iv) 5 + 2a-3b
(v) 2y – \(\frac { 7 }{ 3 }\) z÷x
(vi) 3p x q ÷ z
(vii) 12z ÷ 5x + 4
(viii) 12 – 5z – 4
(ix) a³ – 3ab² x c
Solution:

Question 3.
Write the coefficient of:
(i) xy in – 3axy
(ii) z² in p²yz²
(iii) mn in -mn
(iv) 15 in – 15p²
Solution:

Question 4.
For each of the following monomials, write its degree :
(i) 7y
(ii) – x²y
(iii) xy²z
(iv) – 9y²z³
(v) 3 m³n⁴
(vi) – 2p²q³r⁴
Solution:

Question 5.
Write the degree of each of the following polynomials :
(i) 3y³-x²y² + 4x
(ii) p³q² – 6p²q⁵ + p⁴q⁴
(iii) – 8mn⁶+ 5m³n
(iv) 7 – 3x²y + y²
(v) 3x – 15
(vi) 2y²z + 9yz³
Solution:

Question 6.
Group the like term together :
(i) 9x², xy, – 3x², x² and – 2xy
(ii) ab, – a²b, – 3ab, 5a²b and – 8a²b
(iii) 7p, 8pq, – 5pq – 2p and 3p
Solution:

Question 7.
Write numerical co-efficient of each of the followings :
(i) y
(ii) -y
(iii) 2x²y
(iv) – 8xy³
(v) 3py²
(vi) – 9a²b³
Solution:

Question 8.
In -5x³y²z⁴; write the coefficient of:
(i) z²
(ii) y²
(iii) yz²
(iv) x³y
(v) -xy²
(vi) -5xy²z
Also, write the degree of the given algebraic expression.
Solution:

EXERCISE 11 (B)

Question 1.
Fill in the blanks :
(i) 8x + 5x = ………
(ii) 8x – 5x =……..
(iii) 6xy² + 9xy² =……..
(iv) 6xy² – 9xy² = ………
(v) The sum of 8a, 6a and 5b = ……..
(vi) The addition of 5, 7xy, 6 and 3xy = …………
(vii) 4a + 3b – 7a + 4b = ……….
(viii) – 15x + 13x + 8 = ………
(ix) 6x²y + 13xy² – 4x²y + 2xy² = ……..
(x) 16x² – 9x² = and 25xy² – 17xy²=………

Solution :

Question 2.
Add :
(i)- 9x, 3x and 4x
(ii) 23y², 8y² and – 12y²
(iii) 18pq – 15pq and 3pq

Solution:

Question 3.
Simplify :
(i) 3m + 12m – 5m
(ii) 7n² – 9n² + 3n²
(iii) 25zy—8zy—6zy
(iv) -5ax² + 7ax² – 12ax²
(v) – 16am + 4mx + 4am – 15mx + 5am
Solution:

Question 4.
Add :
(i) a + b and 2a + 3b
(ii) 2x + y and 3x – 4y
(iii)- 3a + 2b and 3a + b
(iv) 4 + x, 5 – 2x and 6x
Solution:

Question 5.
Find the sum of:
(i) 3x + 8y + 7z, 6y + 4z- 2x and 3y – 4x + 6z
(ii) 3a + 5b + 2c, 2a + 3b-c and a + b + c.
(iii) 4x²+ 8xy – 2y² and 8xy – 5y² + x²
(iv) 9x² – 6x + 7, 5 – 4x and 6 – 3x²
(v) 5x² – 2xy + 3y² and – 2x² + 5xy + 9y²
and 3x² -xy- 4y²
(vi) a² + b² + 2ab, 2b² + c² + 2bc
and 4c²-a² + 2ac
(vii) 9ax – 6bx + 8, 4ax + 8bx – 7
and – 6ax – 46x – 3
(viii) abc + 2 ba + 3 ac, 4ca – 4ab + 2 bca
and 2ab – 3abc – 6ac
(ix) 4a² + 5b² – 6ab, 3ab, 6a² – 2b²
and 4b² – 5 ab
(x) x² + x – 2, 2x – 3x² + 5 and 2x² – 5x + 7
(xi) 4x³ + 2x² – x + 1, 2x³ – 5x²– 3x + 6, x² + 8 and 5x³ – 7x
Solution:

Question 6.
Find the sum of:
(i) x and 3y
(ii) -2a and +5
(iii) – 4x² and +7x
(iv) +4a and -7b
(v) x³+3x²y and 2y²
(vi) 11 and -by
Solution:

Question 7.
The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.
Solution:

Question 8.
The two adjacent sides of a rectangle are 6a + 96 and 8a – 46. Find its, perimeter.
Solution

Question 9.
Subtract the second expression from the first:

Solution:

Question 10.
Subtract:

Solution:

Question 11.
Subtract – 5a² – 3a + 1 from the sum of 4a² + 3 – 8a and 9a – 7.
Solution:

Question 12.
By how much does 8x³ – 6x² + 9x – 10 exceed 4x³ + 2x² + 7x -3 ?
Solution:

Question 13.
What must be added to 2a³ + 5a – a² – 6 to get a² – a – a³ + 1 ?
Solution:

Question 14.
What must be subtracted from a² + b² + lab to get – 4ab + 2b² ?
Solution:

Question 15.
Find the excess of 4m² + 4n² + 4p² over m²+ 3n² – 5p²
Solution:

Question 16.
By how much is 3x³ – 2x²y + xy² -y³ less than 4x³ – 3x²y – 7xy² +2y³
Solution:

Question 17.
Subtract the sum of 3a² – 2a + 5 and a² – 5a – 7 from the sum of 5a² -9a + 3 and 2a – a² – 1
Solution:

Question 18.
The perimeter of a rectangle is 28x³+ 16x² + 8x + 4. One of its sides is 8x² + 4x. Find the other side
Solution:

Question 19.
The perimeter of a triangle is 14a² + 20a + 13. Two of its sides are 3a² + 5a + 1 and a² + 10a – 6. Find its third side.
Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.
Simplify:

Solution:

EXERCISE 11 (C)

Question 1.
Multiply:

Solution:

Question 2.
Copy and complete the following multi-plications :

Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Evaluate:

Solution:

Question 5.
Evaluate :

Solution:

Question 6.
Multiply:

Solution:

Question 7.
Multiply:

Solution:

EXERCISE 11 (D)

Question 1.
Divide:

Solution:

Question 2.
Divide :

Solution:

Question 3.
The area of a rectangle is 6x²– 4xy – 10y² square unit and its length is 2x + 2y unit. Find its breadth
Solution:

Question 4.
The area of a rectangular field is 25x² + 20xy + 3y² square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.
Solution:

Question 5.
Divide:

Solution:

EXERCISE 11 (E)

Simplify
Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Question 26.

Solution:

EXERCISE 11 (F)

Enclose the given terms in brackets as required :

Question 1.
 x – y – z = x-{…….)
Solution:

Question 2.
x² – xy² – 2xy – y² = x² – (…….. )
Solution:

Question 3.
4a – 9 + 2b – 6 = 4a – (…….. )
Solution:

Question 4.
x² -y² + z² + 3x – 2y = x² – (…….. )
Solution:

Question 5.
– 2a² + 4ab – 6a²b² + 8ab² = – 2a (……… )
Solution:

Simplify :

Question 6.
2x – (x + 2y- z)
Solution:

Question 7.
p + q – (p – q) + (2p – 3q)
Solution:

Question 8.
9x – (-4x + 5)
Solution:

Question 9.
6a – (- 5a – 8b) + (3a + b)
Solution:

 Question 10.
(p – 2q) – (3q – r)
Solution:

Question 11.
9a (2b – 3a + 7c)
Solution:

Question 12.
-5m (-2m + 3n – 7p)
Solution:

Question 13.
-2x (x + y) + x²
Solution:

Question 14.

Solution:

Question 15.
8 (2a + 3b – c) – 10 (a + 2b + 3c)
Solution:

Question 16.

Solution:

Question 17.
5 x (2x + 3y) – 2x (x – 9y)
Solution:

Question 18.
a + (b + c – d)
Solution:

Question 19.
5 – 8x – 6 – x
Solution:

Question 20.
2a + (6- \(\overline { a-b }\) )
Solution:

Question 21.
3x + [4x – (6x – 3)]
Solution:

Question 22.
5b – {6a + (8 – b – a)}
Solution:

Question 23.
2x-[5y- (3x -y) + x]
Solution:

Question 24.
6a – 3 (a + b – 2)
Solution:

Question 25.
8 [m + 2n-p – 7 (2m -n + 3p)]
Solution:

Question 26.
{9 – (4p – 6q)} – {3q – (5p – 10)}
Solution:

Question 27.
2 [a – 3 {a + 5 {a – 2) + 7}]
Solution:

Question 28.
5a – [6a – {9a – (10a – \(\overline { 4a-3a }\)  )}]
Solution:

Question 29.
9x + 5 – [4x – {3x – 2 (4x – 3)}]
Solution:

Question 30.
(x + y – z)x + (z + x – y)y – (x + y – z)z
Solution:

Question 31.
-1 [a-3 {b -4 (a-b-8) + 4a} + 10]
Solution:

Question 32.

Solution:

Question 33.
10 – {4a – (7 – \(\overline { a-5 }\)) – (5a – \(\overline { 1+a }\))}
Solution:

Question 34.
7a- [8a- (11a-(12a- \(\overline { 6a-5a }\))}]
Solution:

Question 35.

Solution:

Question 36.
x-(3y- \(\overline { 4z-3x }\) +2z- \(\overline { 5y-7x }\))
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 17 Idea of Speed, Distance and Time

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 17 Idea of Speed, Distance and Time

Idea of Speed, Distance and Time Exercise 17A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A train covers 51 km in 3 hours. Calculate its speed. How far does the train go in 30 minutes?
Solution:

Question 2.
A motorist travelled the distance between two towns, which is 65 km, in 2 hours and 10 minutes. Find his speed in metre per minute.
Solution:

Question 3.
A train travels 700 metres in 35 seconds. What is its speed in km/h?
Solution:

Question 4.
A racing car covered 600 km in 3 hours 20 minutes. Find its speed in metre per second. How much distance will the car cover in 50 sec?
Solution:

Question 5.
Rohit goes 350 km in 5 hours. Find :
(i) his speed
(ii) the distance covered by Rohit in 6.2 hours
(iii) the time taken by him to cover 210 km.
Solution:

Question 6.
A boy drives his scooter with a uniform speed of 45 km/h. Find :
(i) the distance covered by him in 1 hour 20 min.
(ii) the time taken by him to cover 108 km.
(iii) the time taken to cover 900 m.
Solution:

Question 7.
I travel a distance of 10 km and come back in 2\(\frac { 1 }{ 2 }\) hours. What is my speed?
Solution:

Question 8.
A man walks a distance of 5 km in 2 hours. Then he goes in a bus to a nearby town, which is 40 km, in further 2 hours. From there, he goes to his office in an autorickshaw, a distance of 5 km, in \(\frac { 1 }{ 2 }\) hour. What was his average speed during the whole journey?
Solution:

Question 9.
Jagan went to another town such that he covered 240 km by a car going at 60 kmh^-1. Then he covered 80 km by a train, going at 100 kmh^-1 and the rest 200 km, he covered by a bus, going at 50 kmh^-1. What was his average speed during the whole journey?
Solution:

Question 10.
The speed of sound in air is about 330 ms^-1. Express this speed in kmh^-1. How long will the sound take to travel 99 km?
Solution:

Idea of Speed, Distance and Time Exercise 17B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A train 180 m long is running at a speed of 90 km/h. How long will it take to pass a railway signal?
Solution:

Question 2.
A train whose length is 150 m, passes a telegraph pole in 10 sec. Find the speed of the train in km/h.
Solution:

Question 3.
A train 120 m long passes a railway platform 160 m long in 14 sec. How long will it take to pass another platform which is 100 m long?
Solution:

Question 4.
Mr. Amit can walk 8 km in 1 hour 20 minutes.
(a) How far does he go in :
(i) 10 minutes?
(ii) 30 seconds?
(b) How long will it take him to walk :
(i) 2500 m?
(ii) 6.5 km?
Solution:

Question 5.
Which is greater : a speed of 45 km/h or a speed of 12.25 m/sec?
How much is the distance travelled by each in 2 seconds?
Solution:

Question 6.
A and B start from the same point and at the same time with speeds 15 km/h and 12 km/h respectively, find the distance between A and B after 6 hours if both move in :
(i) same direction
(ii) the opposite directions.
Solution:

Question 7.
A and B start from the same place, in the same direction and at the same time with speeds 6 km/h and 2 m/sec respectively. After 5 hours who will be ahead and by how much?
Solution:

Question 8.
Mohit covers a certain distance in 6 hrs by his scooter at a speed of 40 kmh^-1.
(i) Find the time taken by Manjoor to cover the same distance by his car at the speed of 60 kmh^-1.
(ii) Find the speed of Joseph, if he takes 8 hrs to complete the same distance.
Solution:

Question 9.
A boy swims 200 m in still water and then returns back to the point of start in total 10 minutes. Find the speed of his swim in
(i) ms^-1
(ii) kmh^-1.
Solution:

Question 10.
A distance of 14.4 km is covered in 2 horus 40 minutes. Find the speed in ms^-1. With this speed Sakshi goes to her school, 240 m away from her house and then returns back. How much time, in all, will Sakshi take?
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 16 Percent (Percentage)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 16 Percent (Percentage)

Percent Exercise 16A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in the percentage form :
(i) 13 out of 20
(ii) 21 eggs out of 30 are good
Solution:

Question 2.
Express the following fractions as percent :

Solution:

Question 3.
Express as percent:
(i) 0.10
(ii) 0.02
(iii) 0.7
(iv) 0.15
(v) 0.032
Solution:

Question 4.
Convert into fractions in their lowest terms:
(i) 8%
(ii) 20%
(iii) 85%
(iv) 250%
(v) 12\(\frac { 1 }{ 2 }\) %
Solution:

Question 5.
Express as decimal fractions :
(i) 25%
(ii) 108%
(iii) 95%
(iv) 4.5%
(v) 29.2%
Solution:

Question 6.
Express each of the following natural numbers as percent :
(i) 7
(ii) 2
(iii) 19.5
(iv) 5.37
Solution:

Percent Exercise 16B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express :
(i) Rs 5 as a percentage of Rs 25.
(ii) 80 paise as a percent of Rs 4.
(iii) 700 gm as a percentage of 2.8 kg.
(iv) 90 cm as a percent of 4.5 m.
Solution:

Question 2.
Express the first quantity as a percent of the second :
(i)) 40 P, ₹ 2
(ii) 500 gm, 6 kg
(iii) 42 seconds, 6 minutes
Solution:

Question 3.
Find the value of each of the following:
(i) 20% of ₹ 150
(ii) 90% of 130
(iii) 15% of 2 minutes
(iv) 7.5 % of 500 kg.
Solution:

Question 4.
If a man spends 70% of his income, what percent does he save ?
Solution:

Question 5.
A girl gets 65 marks out of 80. What percent marks did she get?
Solution:

Question 6.
A class contains 25 children, of which 6 are girls. What percentage of the class are the boys.
Solution:

Question 7.
A tin contains 20 litres of petrol. Due to leakage, 3 litres of petrol is lost. What percent is still present in the tin?
Solution:

Question 8.
An alloy of copper and zinc contains 45% copper and the rest is zinc. Find the weight of zinc in 20 kg of the alloy.
Solution:

Question 9.
A boy got 60 out of 80 in Hindi, 75 out of 100 in English and 65 out of 70 in Arithmetic. In which subject his percentage of marks the best ? Also, find his overall percentage.
Solution:

Question 10.
In a camp, there were 500 soldiers. 60 more soldiers joined them. What percent of the earlier (original) number have joined the camp.
Solution:

Question 11.
In a plot of ground of area 6000 sq. m, only 4500 sq. m is allowed for construction. What percent is to be left without construction?
Solution:

Question 12.
Mr. Sharma has a monthly salary of ₹ 8,000. If he spends ₹ 6,400 every month; find :
(i) his monthly expenditure as percent.
(ii) his monthly savings as percent.
Solution:

Question 13.
The monthly salary of Rohit is ₹ 24,000. If his salary increases by 12%, find his new monthly salary
Solution:

Question 14.
In a sale, the price of an article is reduced by 30%. If the original price of the article is ₹ 1,800, find :
(i) the reduction in the price of the article
(ii) reduced price of the article.
Solution:

Question 15.
Evaluate :
(i) 30% of 200 + 20% of 450 – 25% of 600
(ii) 10% of ₹ 450 – 12% of ₹ 500 + 8% of ₹ 500.
Solution:

Percent Exercise 16C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The price of rice rises from Rs. 30 per kg to Rs. 36 per kg. Find the percentage rise in the price of rice.
Solution:

Question 2.
The population of a small locality was 4000 in 1979 and 4500 in 1981, By what percent had the population increase ?
Solution:

Question 3.
The price of a scooter was ₹ 8000 in 1975. It came down to ₹ 6000 in 1980. By what percent had the price of the scooter came down?
Solution:

Question 4.
Find the resulting quantity when :
(i) ₹ 400 is decreased by 8%.
(ii) 25 km is increased by 5%.
(iii) a speed of 600 km/h is increased by 12\(\frac { 1 }{ 2 }\) %
(iv) there is 2.5% increase in a salary of ₹ 62, 500.
Solution:

Question 5.
The population of a village decreased by 12%. If the original population was 25,000, find the population after decrease?
Solution:

Question 6.
Out of a salary of Rs. 13,500,1 keep 1/3 as savings. Of the remaining money, I spend 50% on food and 20% on house rent. How much do I spend on food and house rent?
Solution:

Question 7.
A tank can hold 50 litres of water. At present, it is only 30% full. How many litres of water shall I put into the tank so that it becomes 50% full?
Solution:

Question 8.
In an election, there are a total of 80,000 voters and two candidates, A and B. 80% of the voters go to the polls out of which 60% vote for A. How many votes does B get.
Solution:

Question 9.
70% of our body weight is made up of water. Find the weight of water in the body of a person whose body weight is 56 kg.
Solution:

Question 10.
Only one-fifth of water is available in liquid form. This limited amount of water is replenished and used by man recurrently. Express this information as percent, showing :
(i) water available in liquid form.
(ii) water available in frozen form.
Solution:
<

Question 11.
By weight, 90% of tomato and 78% of potato is water. Find :
(i) the weight of water in 25 kg of tomato.
(ii) the total quantity, by weight, of water in 90 kg of potato and 30 kg of tomato
(iii) the weight of potato which contains 39 kg of water.
Solution:

Percent Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Rohit’s age is 12 years and Geeta’s age is 15 years. Express :
(i) Rohit’s age as a percent of Geeta’s age.
(ii) Geeta’s age as a percent of Rohit’s age.
Solution:

Question 2.
A class has 30 boys and 20 girls. Find:
(i) the percentage of girls in the class
(ii) the percentage of boys in the class
(iii) percentage of number of boys as compared with number of girls.
Solution:

Question 3.
Mrs. Sharma went to the market with ₹ 800 in her purse. When she returned to her home, ₹ 240 were still left in her purse. What percent of her money did she spend in the market?
Solution:

Question 4.
In a mixture of two liquids A and B, 35% is liquid B. If the total quantity of the mixture is 20 kg, find the quantity of A, by weight.
Solution:

Question 5.
A girl got 375 marks out of 500 in the first term examination, 560 marks out of 800 in the second term examination and 840 marks out of 1200 in the third term examination. Find:
(i) her percentage score in the first term examination.
(ii) her percentage score in the second term examination.
(iii) her percentage score in the third term examination.
(iv) the total marks secured in all the three examinations.
(v) the total marks scored in all the three examinations.
(vi) her percentage score on the whole in all the three examinations.
Solution:

Question 6.
Out of his monthly income of ₹ 2,500; a man spends ₹ 1,750. What percent of his income does he save every month?
Solution:

Question 7.
Mr. Singh’s monthly salary is ₹ 15,000. This month he was promoted with an increment of ₹ 3,000 in his salary. Express his increment as a percent of his original salary.
Solution:

Question 8.
(i) The price of an article increased from ₹ 16 to ₹ 20 ; find the percentage increase.
(ii) The price of an article decreased from Rs 20 to Rs 16 ; find the percentage decrease.
Solution:

Question 9.
(i)) The salary of a man is ₹ 7,200 per month, which is now increased by 8%. Find his new salary per month.
(ii) The salary of Mr. Sahni is ₹ 8,400 per month, which is now decreased by 8%. Find his new salary per month.
Solution:

Question 10.
Find the percentage change from the first quantity to the second :
(i) ₹ 80, ₹ 120
(ii) 75 kg, 60 kg
(iii) 50 cm, 45 cm
Solution:

Question 11.
The original price of an article is ₹ 640. Find its new price when its price is :
(i) increased by 30%
(ii) decreased by 20%
Solution:

Question 12.
Find the number that is :
(i) 50% more than 48
(ii) 30% less than 70
Solution:

Question 13.
Evaluate :
(i) 8% of 900 – 12% of 750 + 20% of 165.
(ii) 70% of 70 + 90% of 90 – 120% of 120.
Solution:

Question 14.
Approximately 97.3% water on the earth is not fit for drinking. Find :
(i) the percentage of water on the earth that is fit for drinking.
(ii) The total volume of water available in certain part of the earth where there is 21,600 m3 of drinking water.
Solution:

Question 15.
Air is an important inexhaustible natural resource. It is essential for the survival of human beings, microbes, plants and animals. The following table shows the percentage of various gases in air.

(i) In 800 m3 of air, calculate the approximate quantities of nitrogen, oxygen and other gases.
(ii) If a certain quantity (by volume) of air contains 4,200 litres of oxygen, find the total quantity of air taken and the amount of nitrogen in it.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 34 Mean and Median

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 34 Mean and Median

Mean and Median Exercise 34A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the mean of :
(i) 7,10, 4 and 17
(ii) 12, 9, 6,11 and 17
(iii) 3, 1, 5, 4, 4 and 7
(iv) 7, 5, 0, 3, 0, 6, 0, 9, 1 and 4
(v) 2.1, 4.5, 5.2, 7.1 and 9.3
(vi) 5, 2.4, 6.2, 8.9, 4.1 and 3.4
Answer:

Question 2.
Find the mean of :
(i) first eight natural numbers
(ii) first six even natural numbers
(iii) first five odd natural numbers
(iv) all prime numbers upto 30
(v) all prime numbers between 20 and 40.
Answer:

Question 3.
Height (in cm) of 7 boys of a locality are 144 cm, 155 cm, 168 cm, 163 cm, 167 cm, 151 cm and 158 cm. Find their mean height.
Answer:

Question 4.
Find the mean of 35, 44, 31, 57, 38, 29, 26,36, 41 and 43.
Answer:

Question 5.
The mean of 18, 28, x, 32, 14 and 36 is 23. Find the value of x.
Answer:

Question 6.
If the mean of x, x + 2, x + 4, x + 6 and x + 8 is 13, find the value of x.
Answer:

Mean and Median Exercise 34B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the median of
(i) 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25
(ii) 3.2, 4.8, 5.6, 5.6, 7.3, 8.9 and 91
(iii) 17, 23, 36, 12, 18, 23, 40 and 20
(iv) 26, 33, 41, 18, 30, 22, 36, 45 and 24
(v) 80, 48, 66, 61, 75, 52, 45 and 70
Solution:

Question 2.
Find the mean and the median of :
(i) 1,3,4, 5, 9, 9 and 11
(ii) 10,12, 12, 15, 15, 17, 18, 18, 18 and 19
(iii) 2, 4, 5, 8, 10,13 and 14
(iv) 5, 8, 10, 11,13, 16, 19 and 20
(v) 1.2, 1.9, 2.2, 2.6 and 2.9
(vi) 0.5, 5.6, 3.8, 4.9, 2.7 and 4.4.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)

Fractions Exercise 3A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Classify, each fraction given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction :

Solution:

Question 2.
Express the following improper fractions as mixed fractions :

Solution:

Question 3.
Express the following mixed fractions as improper fractions :

Solution:

Question 4.
Reduce the given fractions to lowest terms

Solution:

Question 5.
State : true or false

Solution:

Question 6.
Distinguish each of the following fractions, given below, as a simple fraction or a complex fraction :

Solution:

Fractions Exercise 3B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
For each pair, given below, state whether it forms like fractions or unlike fractions :

Solution:

Question 2.
Convert given fractions into fractions with equal denominators :

Solution:

Question 3.
Convert given fractions into fractions with equal numerators :

Solution:

Question 4.
Put the given fractions in ascending order by making denominators equal :

Solution:

Question 5.
Arrange the given fractions in descending order by making numerators equal :

Solution:

Question 6.
Find the greater fraction :


Solution:

Question 7.
Insert one fraction between :

Solution:

Question 8.
Insert three fractions between

Solution:

Question 9.
Insert two fractions between

Solution:

Fractions Exercise 3C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Reduce to a single fraction :


Solution:

Question 2.
Simplify :

Solution:

Question 3.
Subtract :

Solution:

Question 4.
Find the value of

Solution:

Question 5.
Simplify and reduce to a simple fraction :


Solution:

Question 6.
A bought 3 \(\frac { 3 }{ 4 }\) kg of wheat and 2 \(\frac { 1 }{ 2 }\) kg of rice. Find the total weight of wheat and rice bought.
Solution:

Question 7.
Which is greater,\(\frac { 3 }{ 5 }\) or \(\frac { 7 }{ 10 }\) and by how much?
Solution:

Question 8.
What number should be added to 8 \(\frac { 2 }{ 3 }\) to 12 \(\frac { 5 }{ 6 }\)
Solution:

Question 9.
What should be subtracted from 8\(\frac { 3 }{ 4 }\) to get 2 \(\frac { 2 }{ 3 }\)
Solution:

Question 10.
A field is 16 \(\frac { 1 }{ 2 }\) m long and 12 \(\frac { 2 }{ 5 }\) m wide. Find the perimeter of the field.
Solution:

Question 11.
Sugar costs ₹37 \(\frac { 1 }{ 2 }\)per kg. Find the cost of 8\(\frac { 3 }{ 4 }\) kg sugar.
Solution:

Question 12.
A motor cycle runs 31\(\frac { 1 }{ 4 }\) km consuming 1 litre of petrol. How much distance will it run consuming 1\(\frac { 3 }{ 5 }\) liter of petrol?
Solution:

Question 13.
A rectangular park has length = 23 \(\frac { 2 }{ 3 }\) m and breadth = 16 \(\frac { 2 }{ 3 }\) m. Find the area of the park.
Solution:

Question 14.
Each of 40 identical boxes weighs 4 \(\frac { 4 }{ 5 }\) kg Find the total weight of all the boxes.
Solution:

Question 15.
Out of 24 kg of wheat, \(\frac { 5 }{ 6 }\) th of wheat is consumed. Find, how much wheat is still left?
Solution:

Question 16.
A rod of length 2 \(\frac { 2 }{ 5 }\) metre is divided into five equal parts. Find the length of each part so obtained.
Solution:

Question 17.
IfA = 3\(\frac { 3 }{ 8 }\) and B = 6\(\frac { 5 }{ 8 }\) find :
(i) A+B
(ii) B A
Solution:

Question 18.
Cost of 3 \(\frac { 5 }{ 7 }\) litres of oil is ₹83 \(\frac { 1 }{ 2 }\). Find the
cost of one litre oil.
Solution:

Question 19.
The product of two numbers is 20 \(\frac { 5 }{ 7 }\). If one of these numbers is 6 \(\frac { 2 }{ 3 }\), find the other.
Solution:

Question 20.
By what number should 5 \(\frac { 5 }{ 6 }\) be multiplied 1 to get 3\(\frac { 1 }{ 3 }\) ?
Solution:

Fractions Exercise 3D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Simplify
Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Fractions Exercise 3E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is :
(i) The length of AB to that of CD ?
(ii) \(\frac { 1 }{ 2 }\) the length of AB to that of \(\frac { 1 }{ 3 }\) of CD ?
(iii) \(\frac { 1 }{ 5 }\) of CD to that of AB ?
Solution:

Question 2.
Subtract \(\frac { 2 }{ 7 }\) – \(\frac { 5 }{ 21 }\) from the sum of \(\frac { 3 }{ 4 }\) , \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 12 }\)
Solution:

Question 3.
From a sack of potatoes weighing 120 kg, a merchant sells portions weighing 6 kg, 5\(\frac { 1 }{ 4 }\) kg, 9\(\frac { 1 }{ 2 }\) kg and 9\(\frac { 3 }{ 4 }\) kg respectively.
(i) How many kg did he sell ?
(ii) How many kg are still left in the sack ?
Solution:

Question 4.
If a boy works for six consecutive days for 8 hours, 7\(\frac { 1 }{ 2 }\) hours, 8\(\frac { 1 }{ 4 }\) hours, 6 \(\frac { 1 }{ 4 }\)4 3hours, 6\(\frac { 3 }{ 4 }\) hours and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour ?
Solution:

Question 5.
A student bought 4 \(\frac { 1 }{ 3 }\) m of yellow ribbon, 6 \(\frac { 1 }{ 6 }\) m of red ribbon and 3\(\frac { 2 }{ 9 }\) m of blue ribbon for decorating a room. How many metres of ribbon did he buy ?
Solution:

Question 6.
In a business, Ram and Deepak invest \(\frac { 3 }{ 5 }\) and \(\frac { 2 }{ 5 }\) of the total investment. IfRs. 40,000 is the total investment, calculate the amount invested by each ?
Solution:

Question 7.
Geeta had 30 problems for home work. She worked out \(\frac { 2 }{ 5 }\) of them. How many problems were still left to be worked out by her ?
Solution:

Question 8.
A picture was marked at Rs. 90. It was sold at \(\frac { 3 }{ 4 }\) of its marked price. What was the sale price ?
Solution:

Question 9.
Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed 10\(\frac { 1 }{ 2 }\) kg ?Solution:

Question 10.
A rope is 25\(\frac { 1 }{ 2 }\) m long. How many pieces , 1 \(\frac { 1 }{ 2 }\) each of length can be cut out from it?Solution:

Question 11.
The heights of two vertical poles, above the earth’s surface, are 14 \(\frac { 1 }{ 4 }\) m and 22 \(\frac { 1 }{ 3 }\) respectively. How much higher is the second pole as compared with the height of the first pole ?
Solution:

Question 12.
Vijay weighed 65\(\frac { 1 }{ 2 }\) kg. He gained 1\(\frac { 2 }{ 5 }\) kg during the first week, 1 \(\frac { 1 }{ 4 }\) kg during the second week, but lost \(\frac { 5 }{ 16 }\) kg during the 16 third week. What was his weight after the third week ?
Solution:

Question 13.
A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) on house rent, electricity, etc. What fraction of his salary is still left with him ?
Solution:

Question 14.
A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) of the remaining on house rent, electricity, etc. What fraction of his salary is still left with him ?
Solution:

Question 15.
Shyam bought a refrigerator for Rs. 5000. He paid \(\frac { 1 }{ 10 }\) of the price in cash and the rest in 12 equal monthly instalments. How much had he to pay each month ?
Solution:

Question 16.
A lamp post has half of its length in mud, and \(\frac { 1 }{ 3 }\) of its length in water.
(i) What fraction of its length is above the water ?
(ii) If 3\(\frac { 1 }{ 3 }\) m of the lamp post is above the water, find the whole length of the lamp post.
Solution:

Question 17.
I spent \(\frac { 3 }{ 5 }\) of my savings and still have Rs. 2,000 left. What were my savings ?
Solution:

Question 18.
In a school, \(\frac { 4 }{ 5 }\) of the children are boys. If the number of girls is 200, find the number of boys.
Solution:

Question 19.
If \(\frac { 4 }{ 5 }\) of an estate is worth Rs. 42,000, find the worth of whole estate. Also, find the value of \(\frac { 3 }{ 7 }\) of it.
Solution:

Question 20.
After going \(\frac { 3 }{ 4 }\) of my journey, I find that I have covered 16 km. How much Journey is still left ?
Solution:

Question 21.
When Krishna travelled 25 km, he found that \(\frac { 3 }{ 5 }\) of his journey was still left. What was the length of the whole journey.
Solution:

Question 22.
From a piece of land, one-third is bought by Rajesh and one-third of remaining is bought by Manoj. If 600 m² land is still left unsold, find the total area of the piece of land.
Solution:

Question 23.
A boy spent \(\frac { 3 }{ 5 }\) of his money on buying 1 cloth and \(\frac { 1 }{ 4 }\) of the remaining on buying shoes. If initially he has ?2,400; how much did he spend on shoes?
Solution:

Question 24.
A boy spent \(\frac { 3 }{ 5 }\) of his money on buying cloth and \(\frac { 1 }{ 4 }\) of his money on buying shoes. If initially he has ?2,400; how much did he spend on shoes?
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 33 Data Handling (Including Pictograph and Bar Graph)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 33 Data Handling (Including Pictograph and Bar Graph)

Data Handling Exercise 33A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Marks scored by 30 students of class VI are as given below :
38, 46, 33, 45, 63, 53, 40, 85, 52, 75, 60, 73, 62, 22, 69, 43, 45, 33, 47, 41, 29, 43, 37, 49, 83, 44, 55, 22, 35 and 45. State :
(i) the highest marks scored.
(ii) the lowest marks scored.
(iii) the range of marks.
Solution:

Question 2.
For the following raw data, form a discrete frequency distribution :
30,32,32, 28,34,34,32,30,30,32,32,34,30,32,32. 28,32,30, 28,30,32,32,30,28 and 30.
Solution:

Question 3.
Define :
(i) data
(ii) frequency of an observation.
Solution:

Question 4.
Rearranage the following raw data in descending order :
5.3, 5.2, 5.1, 5.7, 5.6, 6.0, 5.5, 5.9, 5.8, 6.1, 5.5, 5.8, 5.7, 5.9 and 5.4. Then write the :
(i) highest value
(ii) lowest value
(iii) range of values
Solution:

Question 5.
Represent the following data in the form of a frequency distribution :
52, 56, 72, 68, 52, 68, 52, 68, 52, 60, 56, 72, 56, 60, 64, 56, 48, 48, 64 and 64.
Solution:

Question 6.
In a study of number of accidents per day, the observations for 30 days were obtained as follows :

Solution:

Question 7.
The following data represents the weekly wages (in ₹) of 15 workers in a factory : 900, 850, 800, 850, 800, 750, 950, 900, 950, 800, 750, 900, 750, 800 and 850.
Prepare a frequency distribution table. Now find,
(i) how many workers are getting less than ₹850 per week?
(ii) how many workers are getting more than ₹800 per week?
Solution:

Question 8.
Using the data, given below, construct a frequency distribution table : 9, 17, 12, 20, 9, 18, 25, 17, 19, 9, 12, 9, 12, 18, 17, 19, 20, 25, 9 and 12. Now answer the following :
(i) How many numbers are less than 19?
(ii) How many numbers are more than 20?
(iii) Which of the numbers, given above, is occurring most frequently?
Solution:

Question 9.
Using the following data, construct a frequency distribution table : 46, 44, 42, 54, 52, 60, 50, 58, 56, 62, 50, 56, 54, 58 and 48.
Now answer the following :
(i) What is the range of the numbers?
(ii) How many numbers are greater than 50?
(iii) How many numbers are between 40 and 50?
Solution:

Data Handling Exercise 33B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The sale of vehicles, in a particular city, during the first six months of the year 2016 is shown below :

vehicles sold
Draw a pictograph to represent the above data.
Solution:

Question 2.


Solution:

Question 3.
The following pictograph shows the number of watches manufactured by a factory, in a particular weeks.


Find
(i) on which day were the least number of w atches manufactured?
(ii) total number of watches manufatured in the whole week?
Solution:

Question 4.
The number or animals in five villages are as follows :

Prepare a pitctograph of these animals using one symbol to represent 20 animals.
Solution:

Question 5.
The following pictograph shows different subject books which are kept in a school library.

Taking symbol of one book = 50 books, find :
(i) how many History books are there in the library ?
(ii) how many Science books are there in the library ?
(iii) which books are maximum in number ?
Solution:

Data Handling Exercise 33C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The following table gives the number of students in class VI in a school during academic years 2011-2012 to 2015-2016.

Represent the above data by a bar graph.
Solution:

Question 2.
The attendence of a particular class for the six days of a week are as given below :

Draw a suitable graph.
Solution:

Question 3.
The total number of students present in class VI B, for the six days in a week were as given below. Draw a suitable bar graph.

Solution:

Question 4.
The following table shows the population of a particular city at different years :

Represent the above information with the help of a suitable bar graph.
Solution:

Question 5.
In a survey of 300 families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given below :

Read the graph carefully and answer the following questions :
(i) How many families have 2 children each?
(ii) How many families have no child?
(iii) What percentage of families have 4 children?
Solution:

Question 6.
Use the data, given in the following table, to draw’ a bar graph

Out of A, B, C, D, E and F
(i) Which has the maximum value.
(ii) Which is greater A + D or B + E.
Solution:

Question 7.
The bar graph drawn below shows the number of tickets sold during a fair by 6 students A, B, C, D, E and F.

Using the Bar graph, answer the following questions :
(i) Who sold the least number of tickets?
(ii) Who sold the maximum number of tickets?
(iii) How many tickets were sold by A, B and C taken together?
(iv) How many tickets were sold by D, E and F taken together?
(v) What is the average number of tickets sold per student?
Solution:

Question 8.
The following bar graph shows the number of children, in various classes, in a school in Delhi.

Using the given bar graph, find :
(i) the number of children in each class.
(ii) the total number of children from Class 6 to Class 8.
(iii) how many more children there are in Class 5 compared to Class 6 ?
(iv) the total number of children from Class 1 to Class 8.
(v) the average number of children in a class.
Solution:

Question 9.
The column graph, given above, shows the number of patients, examined by Dr. V.K. Bansal, on different days of a particular week.
Use the graph to answer the following:
(i) On which day were the maximum number of patients examined?
(ii) On which day were the least number of patients examined?
(iii) On which days were an equal number or patients examined?
(iv) What is the total number of patients examined in the week?
Solution:

Question 10.
A student spends his pocket money on various items, as given below :
Books : Rs. 380, Postage : Rs. 30, Cosmetics : Rs. 240, Stationary : Rs. 220 and Entertainment: Rs. 120.
Draw a bar graph to represent his expenses.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Decimal Fractions Exercise 15A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the number of decimal places in each of the following :
(i) 7.03
(ii) 0.509
(iii) 146.2
(iv) 0.0065
(v) 8.03207
Solution:

Question 2.
Convert the given unlike decimal fractions into like decimal fractions:
(i) 1.36, 239.8 and 47.008
(ii) 507.0752, 8.52073 and 0.808
(iii) 459.22, 7.03093 and 0.200037
Solution:

Question 3.
Change each of following fractions to a decimal fraction :

Solution:

Question 4.
Convert into a decimal fraction :

Solution:

Question 5.
Change the given decimals fractions to fractions in their lowest terms :
(i) 0.05
(ii) 3.95
(iii) 4.005
(iv) 0.876
(v) 50.06
(vi) 0.01075
(vii) 4.8806
Solution:

Decimal Fractions Exercise 15B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following :
(i) 0.243, 2.47 and 3.009
(ii) 0.0736, 0.6095 and 0.9107
(iii) 1.01, 257 and 0.200
(iv) 18, 200.35, 11.72 and 2.3
(v) 0.586, 0.0586 and 0.00586
Solution:

Question 2.
Find the value of :
(i) 6.8 – 2.64
(ii) 2 – 1.0304
(iii) 0.1 – 0.08
(iv) 0.83 – 0.342
Solution:

Question 3.
Subtract :
(i) 0.43 from 0.97
(ii) 2.008 from 22.1058
(iii) 0.18 from 0.6
(iv) 1.002 from 17
(v) 83 from 92.05
Solution:

Question 4.
Simplify :
(i) 3.5 – 2.43 + 0.075
(ii) 7.84 + 0.3 – 4.016
(iii) 2.987 – 1.25 – 0.54
(iv) 52.9 – 231.666 + 204
(v) 8.57 – 6.4432 – 1.70 + 0.683
Solution:

Question 5.
From the sum of 75.75 and 4.9 subtract 28.465.
Solution:

Question 6.
Subtract the sum of 8.14 and 12.9 from 32.7.
Solution:

Question 7.
Subtract the sum of 34.27 and 159.8 from the sum of 20.937 and 200.6.
Solution:

Question 8.
From the sum of 2.43 and 4.349 subtract the sum of 0.8 and 3.15.
Solution:

Question 9.
By how much does the sum of 18.0495 and 34.9644 exceed the sum of 7.6752 and 24.876?
Solution:

Question 10.
What least number must be added to 89.376 to get 1000?
Solution:

Decimal Fractions Exercise 15C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Multiply :
(i) 5.6 and 8
(ii) 38.46 and 9
(iii) 0.943 and 62
(iv) 0.0453 and 35
(v) 7.5 and 2.5
(vi) 4.23 and 0.8
(vii) 83.54 and 0.07
(viii) 0.636 and 1.83
(ix) 6.4564 and 1000
(x) 0.076 and 100
Solution:

Question 2.
Evaluate :
(i) 0.0008 x 26
(ii) 0.038 x 95
(iii) 1.2 x 2.4 x 3.6
(iv) 0.9 x 1.8 x 0.27
(v) 1.5 x 1.5 x 1.5
(vi) 0.025 x 0.025
(vii) 0.2 x 0.002 x 0.001
Solution:

Question 3.
Multiply each of the following numbers by 10, 100 and 1000 :
(i) 3.9
(ii) 2.89
(in) 0.0829
(iv) 40.3
(v) 0.3725
Solution:

Question 4.
Evaluate :
(i) 8.64 ÷ 8
(ii) 0.0072 ÷ 6
(iii) 20.64 ÷ 16
(iv) 1.602 ÷ 15
(v) 13.08 ÷ 4
(vi) 3.204 ÷ 9
(vii) 3.024 ÷ 12
(viii) 5.15 ÷ 5
(ix) 3 ÷ 5
Solution:

Question 5.
Divide each of the following numbers by 10,100 and 1000 :
(i) 49.79
(ii) 0.923
(iii) 0.0704
Solution:

Question 6.
Evaluate :
(i) 9.4 ÷ 0.47
(ii) 6.3 ÷ 0.09
(iii) 2.88 ÷ 1.2
(iv) 8.64 ÷ 1.6
(v) 37.188 ÷ 3.6
(vi) 16.5 ÷ 0.15
(vii) 3.2 ÷ 0.005
(viii) 3.24 ÷ 0.0016
Solution:

Question 7.
Fill in the blanks with 10,100,1000, or 10000 etc.:
(i) 7.85 x ………….. = 78.5
(ii) 0.442 x ………. = 442
(in) 0.0924 x ………… = 9.24
(iv) 0.00187 x …………. = 18-7
(v) 2.6 x …………. = 2600
(vi) 0.08 x ………… = 80
(vii) 96.7 ÷ ………….. = 0.967
(viii) 5.2 ÷ ……………. = 0.52
(ix) 33.15 ÷ ……………….. = 0.03315
(x) 0.7 ÷ ………… = 0.007
(xi) 0.00672 x ……… = 67.2
Solution:

Question 8.
Evaluate :
(i) 9.32 – 28.54 ÷ 10
(ii) 0.234 x 10 + 62.8
(iii) 3.06 x 100 – 889.4 ÷ 100
(iv) 2.86 x 7.5 + 45.4 ÷ 0.2
(v) 97.82 x 0.03 – 0.54 ÷ 0.3
Solution:

Decimal Fractions Exercise 15D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express in paise :
(i) Rs. 8.40
(ii) Rs. 0.97
(iii) Rs. 0.09
(iv) Rs. 62.35
Solution:

Question 2.
Express in rupees :
(i) 55 P
(ii) 8 P
(iii) 695 P
(iv) 3279 P
Solution:

Question 3.
Express in centimetre (cm) :
(i) 6 m
(ii) 8.54 m
(iii) 3.08 m
(iv) 0.87 m
(v) 0.03 m
(vi) 25.04 m
Solution:

Question 4.
Express in metre (m) :
(i) 250 cm
(ii) 2328 cm
(iii) 86 cm
(iv) 4 cm
(v) 107 cm
Solution:

Question 5.
Express in gramme (gm) :
(i) 6 kg
(ii) 5.543 kg
(iii) 0.078 kg
(iv) 3.62 kg
(v) 4.5 kg
Solution:

Question 6.
Express in kilogramme (kg) :
(i) 7000 gm
(ii) 6839 gm
(iii) 445 gm
(iv) 8 gm
(iv) 93 gm
(vi) 13545 gm
Solution:

Question 7.
Add (giving answer in rupees) :
(i) Rs. 5.37 and Rs. 12
(ii) Rs. 24.03 and 532 paise
(iii) 73 paise and Rs. 208
(iv) 8 paise and Rs. 1536
Solution:

Question 8.
Subtract :
(i) Rs. 35.74 from Rs. 63.22
(ii) 286 paise from Rs. 7.02
(iii) Rs. 0.55 from 121 paise
Solution:

Question 9.
Add (giving answer in metre) :
(i) 2.4 m and 1.78 m
(ii) 848 cm and 2.9 m
(iii) 0.93 m and 64 cm
Solution:

 

Question 10.
Subtract (giving answer in metre) :
(i) 5.03 m from 19.6 m
(ii) 428 cm from 1033 m
(iii) 0.84 m from 122 cm
Solution:

Question 11.
Add (giving answer in kg) :
(i) 2.06 kg and 57.864 kg
(ii) 778 gm and 1.939 kg
(iii) 0.065 kg and 4023 gm
Solution:

Question 12.
Subtract (giving answer in kg) :
(i) 9.462 kg from 15.6 kg
(ii) 4317 gm from 23 kg
(iii) 0.798 kg from 4169 gm
Solution:

Decimal Fractions Exercise 15E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The cost of a fountain pen is Rs. 13.25. Find the cost of 8 such pens.
Solution:

Question 2.
The cost of 25 identical articles is Rs. 218.25. Find the cost of one article.
Solution:

Question 3.
The length of an iron rod is 10.32 m. The rod is divided into 4 pieces of equal lengths. Find the length of each piece.
Solution:

Question 4.
What will be the total length of cloth required to make 5 shirts, if 2.15 m of cloth is needed for each shirt?
Solution:

Question 5.
Find the distance walked by a boy in 1\(\frac { 1 }{ 2 }\) hours, if he walks at 2.150 km every hour.
Solution:

Question 6.
83 note-books are sold at Rs. 15.25 each. Find the total money (in rupees) obtained by selling these note-books.
Solution:

Question 7.
If length of one bed-cover is 2.1 m, find the total length of 17 bed-covers.
Solution:

Question 8.
A piece of rope is 10 m 67 cm long. Another rope is 16 m 32 cm long. By how much is the second rope longer than the first one?
Solution:

Question 9.
12 cakes of soap together weigh 5 kg and 604 gm. Find the weight of
(i) One cake in both kg and gramme
(ii) 5 cakes in kg.
Solution:

Question 10.
Three strings of lengths 50 m 75 cm; 68 m 58 cm and 121 m 3 cm, respectively, are joined together to get a single string of greatest length, And the length of the single string obtained.
If this single string is then divided into 12 equal pieces ; find the length of each piece.
Solution:

Decimal Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write th& following decimal numbers in ascending order of value
(i) 5.054, 5.250, 5.245 and 5.0543
(ii) 62.443, 62.434, 62.344 and 62.444
Solution:

Question 2.
What number added to 0.805 gives 1?
Solution:

Question 3.
What must be subtracted from 3 to get 2.462?
Solution:

Question 4.
By how much should 83.407 be decreased to get 27.78?
Solution:

Question 5.
Two articles weigh 32.674 kg and 40.038 kg respectively. Find :
(i) the total weight of both the articles.
(ii) the difference in the weights of both the articles.
Solution:

Question 6.
By how much does the sum of 34.07 and 15.239 exceed the sum of 16.40 and 27.08?
Solution:

Question 7.
The cost of 1 kg of fruit is Rs. 27.50. What is the cost of 3.6 kg of fruit?
Solution:

Question 8.
Evaluate :
(i) 0.8 x 0.8 x 0.8
(ii) 0.8 ÷ 0.8 x 0.8
(iii) 0.8 x 0.8 ÷ 0.8
(iv) 0.8 ÷ 0.8 of 0.8
(v) 0.8 of 0.8 ÷ 0.8
Solution:

Question 9.
Evaluate :
(i) 3.5 x (4.2 + 2.6)
(ii) 3.5 x 4.2 + 3.5 x 2.6
Are (i) and (ii) equal ?
Solution:

Question 10.
Evaluate :
(i) (3.87 – 2.09) x 2.4
(ii) 3.87 x 2.4 – 2.09 x 2.4
Are (i) and (ii) equal ?
Solution:

Question 11.
A 4.85 m long pole is divided into 5 equal parts. Find the length of each part.
Solution:

Question 12.
A car can run 16.8 km consuming one litre of petrol. How many kilometres will it run on 3.7 litres of petrol ?
Solution:

Question 13.
A certain amount of money is distributed among 28 persons. If each person gets Rs. 62.45 and Rs. 5.78 is left, find the original amount of money.
Solution:

Question 14.
Complete the following table :

Solution:

Question 15.
The difference between two numbers is 47.364. If the smaller number is 31.855 ; find the bigger one.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 32 Perimeter and Area of Plane Figures

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 32 Perimeter and Area of Plane Figures

Perimeter and Area of Plane Figures Exercise 32A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
What do you understand by a plane closed figure?
Solution:

Question 2.
The interior of a figure is called region of the figure. Is this statement true ?
Solution:

Question 3.
Find the perimeter of each of the following closed figures :
Solution:

Question 4.
Find the perimeter of a rectangle whose:
(i) length = 40 cm and breadth = 35 cm
(ii) length = 10 m and breadth = 8 m
(iii) length = 8 m and breadth = 80 cm
(iv) length = 3.6 m and breadth = 2.4 m
Solution:

Question 5.
If P denotes perimeter of a rectangle, l denotes its length and b denotes its breadth, find :
(i) l, if P = 38cm and b = 7cm
(ii) b, if P = 3.2m and l = 100 cm
(iii) P, if l = 2 m and b = 75cm
Solution:

Question 6.
Find the perimeter of a square whose each side is 1.6 m.
Solution:

Question 7.
Find the side of the square whose pe-rimeter is 5 m.
Solution:

Question 8.
A square field has each side 70 m whereas a rectangular field has length = 50 m and breadth = 40 m. Which of the two fields has greater perimeter and by how much?
Solution:

Question 9.
A rectangular field has length = 160m and breadth = 120 m. Find :
(i) the perimeter of the field.
(ii) the length of fence required to enclose the field.
(iii) the cost of fencing the field at the rate of ? 80 per metre.
Solution:

Question 10.
Each side of a square plot of land is 55 m. Find the cost of fencing the plot at the rate of ₹32 per metre.
Solution:

Question 11.
Each side of a square field is 70 cm. How much distance will a boy walk in order to make ?
(i) one complete round of this field?
(ii) 8 complete rounds of this field?
Solution:

Question 12.
A school playground is rectangular in shape with length = 120 m and breadth = 90 m. Some school boys run along the boundary of the play-ground and make 15 complete rounds in 45 minutes. How much distance they run during this period.
Solution:

Question 13.
Mohit makes 8 full rounds of a rect-angular field with length = 120 m and breadth = 75 m.
John makes 10 full rounds of a square field with each side 100 in. Find who covers larger distance and by how much?
Solution:

Question 14.
The length of a rectangle is twice of its breadth. If its perimeter is 60 cm, find its length.
Solution:

Question 15.
Find the perimeter of :
(i) an equilateral triangle of side 9.8 cm.
(ii) an isosceles triangle with each equal side = 13 cm and the third side = 10 cm.
(iii) a regular pentagon of side 8.2 cm.
(iv) a regular hexagon of side 6.5 cm.
Solution:

Question 16.
An equilateral triangle and d square have an equal perimeter. If the side of the triangle is 9.6 cm; what is the length of the side of the square?
Solution:

Question 17.
A rectangle with length = 18 cm and breadth = 12 cm has same perimeter as that of a regular pentagon. Find the side of the pentagon.
Solution:

Question 18.
A regular pentagon of each side 12 cm has same perimeter as that of a regular hexagon. Find the length of each side of the hexagon.
Solution:

Question 19.
Each side of a square is 45 cm and a rectangle has length 50 cm. If the perimeters of both (square and rectangle) are same, find the breadth of the rectangle.
Solution:

Question 20.
A wire is bent in the form of an equilateral triangle of each side 20 cm. If the same wire is bent in the form of a square, find the side of the square.
Solution:

Perimeter and Area of Plane Figures Exercise 32B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the area of a rectangle whose :
(i) length = 15 cm breadth = 6.4 cm
(ii) Length = 8.5 m breadth = 5 m
(iii) Length = 3.6 m breadth = 90 cm
(iv) Length = 24 cm breadth =180 mm
Solution:

Question 2.
Find the area of a square, whose each side is :
(i) 7.2 cm
(ii) 4.5 m
(iii) 4.1 cm
Solution:

Question 3.
If A denotes area of a rectangle, l represents its length and b represents its breadth, find :
(i) l, if A = 48 cm² and b = 6 cm
(ii) b, if A = 88 m² and l = 8m
Solution:

Question 4.
Each side of a square is 3.6 cm; find its
(i) perimeter
(ii) area.
Solution:

Question 5.
The perimeter of a square is 60 m, find :
(i) its each side its area
(ii) its new area obtained on increasing
(iii) each of its sides by 2 m.
Solution:

Question 6.
Each side of a square is 7 m. If its each side be increased by 3 m, what will be the increase in its area.
Solution:

Question 7.
The perimeter of a square field is numerically equal to its area. Find each side of the square.
Solution:

Question 8.
A rectangular piece of paper has area = 24 cm² and length = 5 cm. Find its perimeter.
Solution:

Question 9.
Find the perimeter of a rectangle whose area = 2600 m² and breadth = 50 m.
Solution:

Question 10.
What will happen to the area of a rectangle, if its length and breadth both are trebled?
Solution:

Question 11.
Length of a rectangle is 30 m and its breadth is 20 m. Find the increase in its area if its length is increased by 10 m and its breadth is doubled.
Solution:

Question 12.
The side of a square field is 16 m. What will be increase in its area, if:
(i) each of its sides is increased by 4 m
(ii) each of its sides is doubled.
Solution:

Question 13.
Each rectangular tile is 40 cm long and 30 cm wide. How many tiles will be required to cover the floor of a room with length = 4.8 m and breadth = 2.4 m.
Solution:

Question 14.
Each side of a square tile is 60 cm. How many tiles will be required to cover the floor of a hall with length = 50 m and breadth = 36 m.
Solution:

Question 15.
The perimeter of a square plot = 360 m. Find :
(i) its area.
(ii) cost of fencing its boundary at the rate of ₹ 40 per metre.
(iii) cost of levelling the plot at ₹60 per square metre.
Solution:

Question 16.
The perimeter of a rectangular field is 500 m and its length = 150 m. Find:
(i) its breadth,
(ii) its area.
(iii) cost of ploughing the field at the rate of ₹1.20 per square metre.
Solution:

Question 17.
The cost of flooring a hall of ₹64 per square metre is ₹2,048. If the breadth of the hall is 5m, find :
(i) its length.
(ii) its perimeter.
(iii) cost of fixing a border of very small width along its boundary at the rate of ₹60 per square metre.
Solution:

Question 18.
The length of a rectangle is three times its breadth. If the area of the rectangle is 1875 sq. cm, find its perimeter.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions