Category: ICSE

ML Aggarwal Class 7 Solutions Chapter 13 Practical Geometry Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress

Question 1.
State whether the following statements are true or false. Justify your answer.
(i) A triangle with lengths of sides 2.5 cm, 3 cm, and 6 cm can be constructed.
(ii) A triangle DEF with EF = 7.2 cm, m∠E = 110° and m∠F = 80° can be constructed.
(iii) If the measure of an acute angle and the length of the hypotenuse of a right-angled triangle are given, then the triangle can be constructed.
Solution:

Question 2.
Draw a line AB and take a point C outside it. Through C, draw a line parallel to AB by using the concept of equal corresponding angles.
Solution:

Question 3.
Draw a triangle PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?
Solution:

Question 4.
Construct a triangle ABC with BC = 7.5 cm, AC = 5 cm and m∠C = 60° by using ruler and compasses only.
Solution:

Question 5.
Construct a triangle ABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm by using ruler and compasses only.
Solution:
Steps of Construction:

Question 6.
Construct an isosceles right angled triangle ABC, with m∠ABC = 90° and AC = 6 cm.
Solution:

ML Aggarwal Class 7 Solutions Chapter 13 Practical Geometry Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions

Higher Order Thinking Skills (HOTS)

Question 1.
Construct a triangle ABC such that BC = 5.2 cm, AB = 4.8 cm and median CM = 3.6 cm.
Solution:

Question 2.
Construct an isosceles right-angled triangle ABC such that its hypotenuse BC = 6 cm.
Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Check Your Progress

Question 1.
State whether the following statements are true (T) or false (F):
(i) The fraction \(\frac{2}{3}\) lies between 2 and 3.
(ii) To find an equivalent fraction to a given fraction, we may add or subtract the same (non-zero) number to its numerator and denominator.
(iii) To add or subtract like fractions, we add or subtract the numerators while keeping the denominator same.
Solution:

Question 2.
How many natural numbers are there between 102 and 112? What fraction of them are prime numbers?
Solution:

Question 3.
Match the equivalent fractions from each row:

Solution:

Question 4.
Replace by an appropriate symbol ‘< or >’ between the given fractions:

Solution:

Question 5.
Arrange the following fractions in descending order : \(\frac{7}{30}, \frac{13}{15}, \frac{9}{10}, \frac{3}{5}\)
Solution:

Question 6.
Simplify: \(2 \frac{1}{2}-3 \frac{1}{4}+5 \frac{5}{6}\)
Solution:

Question 7.
Evaluate the following:

Solution:

Question 8.
Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is \(\frac{5}{6}\) full and Samuel’s shelf is \(\frac{3}{5}\) full. Whose bookshelf is more full and by what fraction?
Solution:

Question 9.
A farmer uses four out of five equal strips of his land for wheat crop and \(\frac{1}{7}\) of his land for cereal crop. What fraction of his land is available for other crops?
Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A fraction is a number which represent a ………… of whole.
(ii) A proper fraction lies between 0 and …………
(iii) A mixed fraction can be converted into ………… fraction.
(iv) Fractions having different denominations are called …………
(v) In two like fractions, the fraction having smaller numerator is …………
(vi) \(\frac{144}{180}\) reduced to simplest form is …………..
(vii) \(7 \frac{2}{5}\) + ………… = 12
(viii) \(\frac{42}{56}=\frac{6}{\dots . .}\)
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Two fractions with same numerator are called like fractions.
(ii) A fraction in which the numerator is greater than is denominator is called an improper fraction.
(iii) Every improper fract on can be converted into a mixed fraction.
(iv) Every fraction can be represented by a point on a number line.
(v) In two unlike fractions with same numerator, the fraction having greater denominator is greater.
(vi) \(\frac{1}{2}, \frac{1}{3} \text { and } \frac{1}{4}\) are like fractions.
(vii) \(5-1 \frac{3}{4}=4 \frac{1}{4}\)
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 17):
Question 3.
In the given figure, the shaded part is represented by the fraction :

Solution:

Question 4.
In the given figure, the shaded region is represented by the fraction :

Solution:

Question 5.
The two consecutive integers between which the fraction \(\frac{5}{7}\) lies are
(a) 5 and 7
(b) 5 and 6
(c) 6 and 7
(d) 0 and 1
Solution:

Question 6.
Which of the following pairs of fractions are not equivalent?

Solution:

Question 7.
The fraction equivalent to \(\frac{45}{81}\) is

Solution:

Question 8.
The fraction which is not equal to \(\frac{4}{5}\) is

Solution:

Question 9.
Which of the following fractions is not in the lowest form?

Solution:

Question 10.
A pair of like fraction is

Solution:

Question 11.
Which of the following fractions is the greatest?

Solution:

Question 12.
Which of the following fractions is the smallest?

Solution:

Question 13.
Which of the following is a false statement?

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.
Anshul eats \(\frac{4}{7}\) of a pizza. The fraction of the pizza left is

Solution:

Question 17.
The fraction whose numerator is the smallest odd prime number and denominator is the smallest composite number is

Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Write all proper fractions whose sum of numerator and denominator is 12.
Solution:

Question 2.
The given figure represents the preferences of the students during breakfast in a hostel mess. If the total number of students in the mess is 540, then with reference to the given figure, answer the following questions:

(i) What is the number of students who prefer coffee?
(ii) Whose number is greater, milk drinkers or
orange juice drinkers and by what number?
(iii) What is the total number of students who drink
mango shake or coffee? Is it equal to milk drinker?
(iv) Is the sum of all fractions in the given figure equal to 1 ?
Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.7 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.7

Question 1.
Sarita bought \(\frac{2}{5}\) metre of ribbon and Laiita \(\frac{3}{4}\) metre of ribbon. What is the total length of the ribbon they bought?
Solution:

Question 2.
A bamboo of length \(2 \frac{3}{4}\) metre broke into two pieces. One piece was \(\frac{7}{8}\) metre long. How long is the other piece?
Solution:

Question 3.
Nidhi’s house is \(1 \frac{9}{10}\) km from her school. She walked some distance and then took a bus for \(1 \frac{1}{2}\) km to reach the school. How far did she walk?
Solution:

Question 4.
From a rope of length \(20 \frac{1}{2}\) m, a piece of length \(3 \frac{5}{8}\) m is cut off. Find the length of the remaining rope.
Solution:

Question 5.
The weight of three packets are \(2 \frac{3}{4}\) kg. \(3 \frac{1}{3}\) kg. and \(5 \frac{2}{5}\) kg. Find total weight of all the three packets.
Solution:

Question 6.
Shivani read 25 pages of a book containing 100 pages. Nandni read \(\frac{2}{5}\) of the same book. Who read less?
Solution:

Question 7.
Rafiq exercised for \(\frac{3}{6}\) of an hour, while Rohit, exercised for \(\frac{3}{4}\) of an hour. Who exercised for a longer time and by what fraction of an hour?
Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.6 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.6

Question 1.
Evaluate the following:

Solution:

Question 2.
Evaluate the following:

Solution:

Question 3.
Find the reciprocal of each of the following
(i) \(\frac{9}{13}\)
(ii) \(2 \frac{3}{8}\)
Solution:

Question 4.
Evaluate the following:

Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.5 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.5

Question 1.
Work out the following :

Solution:

Question 2.
Find in the missing fractions:

Solution:

Question 3.
Work out the following:

Solution:

Question 4.
Simplify the following:

Solution:

Question 5.
(i) What number should be added to \(\frac{5}{12}\) to get \(2 \frac{3}{8}\)?
(ii) What number should be subtracted from 5 to get \(1 \frac{5}{13}\) ?
Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.4

Question 1.
Show the fractions \(\frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{4}{6}, \frac{5}{6}, \frac{6}{6}\) and \(\frac{8}{6}\) on the number line. Replace ‘……’ by an appropriate sign” between given fractions:

Solution:

Question 2.
Compare the given fractions and replace ‘….’ by an appropriate sign ”

Solution:

Question 3.
Replace ‘…..’ by an appropriate sign ‘<, = or >’ between the given fractions:

Solution:

Question 4.
Write the shaded portions as fractions. Arrange them in ascending order using appropriate sign between fractions:

Solution:

Question 5.
Compare the following pairs of fractions:

Solution:

Question 6.
Fill in the boxes by the symbol < or > to make the given statements true:

Solution:

Question 7.
Arrange the given fractions in descending order:

Solution:

Question 8.
Arrange the given fractions in the ascending order:

Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.3

Question 1.
State which of the following fractions are proper, improper or mixed:

Solution:

Question 2.
Convert the following improper fractions into mixed numbers:

Solution:

Question 3.
Convert the following mixed number into improper fractions:

Solution:

Question 4.
Write the fractions representing the shaded regions. Are all these fractions equivalent?

Solution:

Question 5.
Write the fractions representing the shaded regions and pair up the equivalent fractions from each row:


Solution:

Question 6.
(i) Find the equivalent fraction of \(\frac{15}{35}\) with denominator 7.
(ii) Find the equivalent fraction of \(\frac{2}{9}\) with denominator 63.
Solution:

Question 7.
Find the equivalent fraction of \(\frac{3}{5}\) having
(i) denominator 30
(ii) numerator 27.
Solution:

Question 8.
Replace ‘…..’ in each of the following by the correct number.

Solution:

Question 9.
Check whether the given pairs of fractions are equivalent:

Solution:

Question 10.
Reduce the following fractions to simplest form:

Solution:

Question 11.
Convert the following fractions into equivalent like fractions:

Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.2

Question 1.
Show the fractions \(\frac{2}{5}, \frac{3}{5}, \frac{4}{5} \text { and } \frac{5}{5}\) on a number line.
Solution:

Question 2.
Show \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8} \text { and } \frac{7}{8}\) on a number line.
Solution:

Question 3.
Show \(\frac{0}{10}, \frac{1}{10}, \frac{3}{10}, \frac{5}{10}, \frac{7}{10} \text { and } \frac{10}{10}\) on a number line.
Solution:

ML Aggarwal Class 6 Solutions Chapter 6 Fractions Ex 6.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.1

Question 1.
Write the following division as fractions:
(i) 3 ÷ 7
(ii) 11 ÷ 78
(iii) 113 ÷ 128
Solution:

Question 2.
Write the following fractions in words.
(i) \(\frac{2}{7}\)
(ii) \(\frac{3}{10}\)
(iii) \(\frac{15}{28}\)
Solution:

Question 3.
Write the following fractions in number form:
(i) one – sixth
(ii) three – eleventh,
(iii) seven-fortieth
(iv) thirteen – one hundred twenty fifth
Solution:

Question 4.
What fraction of each of the following is shaded part?

Solution:

Question 5.
Shade the parts of the following figures according to given fractions:

Solution:

Question 6.
In the adjoining figure, if we say that the shaded region is \(\frac{1}{4}\) of the whole region, then identify the error in it.

Solution:

Question 7.
Write the fraction in which
(i) numerator = 5 and denominator = 13
(ii) denominator = 23 and numerator = 17
Solution:

Question 8.
Shabana has to stitch 35 dresses. So, ar she has stitched 21 dresses. What fraction of dresses has she stitched?
Solution:

Question 9.
What fraction of a day is 8 hours ?
Solution:

Question 10.
What fraction of an hour is 45 minutes ?
Solution:

Question 11.
How many natural numbers are there from 87 to 97? What fraction of them are prime numbers?
Solution: