# CBSE Important Questions Class 6 Maths Chapter 7

## Important Questions Class 6 Maths Chapter 7 – Fractions

Maths is a major subject taught in school, but it is a subject that is needed in our everyday life too.

Chapter 7 of Class 6 Maths is about fractions. Students are familiar with fractions. In simple words, a fraction represents a part of the whole. It has a numerator and denominator. Generally, the numerator is smaller than the denominator, but the opposite happens too. Students must practise questions from the chapter to clarify their understanding of these concepts.

Extramarks is a leading company that provides unlimited study materials to students. Our experts have prepared the Important Questions Class 6 Maths Chapter 7 to help students practise. They have collected several questions and provided the solutions here. Thus, it will help students clear any doubts that they have.

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### CBSE Important Questions for Class 6 Maths

Sr No Chapter No Chapter Name
1 Chapter 1 Knowing Our Numbers
2 Chapter 2 Whole Numbers
3 Chapter 3 Playing with Numbers
4 Chapter 4 Basic Geometrical Ideas
5 Chapter 5 Understanding Elementary Shapes
6 Chapter 6 Integers
7 Chapter 7 Fractions
8 Chapter 8 Decimals
9 Chapter 9 Data Handling
10 Chapter 10 Mensuration
11 Chapter 11 Algebra
12 Chapter 12 Ratio and Proportion
13 Chapter 13 Symmetry
14 Chapter 14 Practical Geometry

## Important Questions Class 6 Maths Chapter 7 – With Solutions

The experts of Extramarks have collected the following questions from different sources. They have taken help from the textbook exercises, NCERT exemplar and important reference books. Apart from this, they have also included some questions from CBSE past years’ question papers and CBSE sample papers so that students may know which types of questions generally come in exams. Thus, students may follow the Important Questions Class 6 Maths Chapter 7 to boost their exam preparation. The questions are-

Question 1. Write the fraction representing the shaded portion:
Answer 1. Total number of parts = 4

Fraction of shaded parts = 2/4

Question 2. Write the fraction representing the shaded portion:

Answer 2. Total number of parts = 9

Fraction of shaded parts = 4/9

Question 3. Write the fraction representing the shaded portion:

Answer 3. Total number of parts = 8

Fraction of shaded parts = 4/8

Question 4. What fraction of a day are eight hours?

Answer 4. Total number of hours in a day = 24

Therefore, the fraction of 8 hours = 8/24 or 1/3

Question 5. What fraction of an hour are 40 minutes?

Answer 5. Minutes in an hour = 60

Therefore, a fraction of 40 minutes = 40/60 or 2/3.

Question 6. Arya, Abhimanyu and Vivek shared lunch today. Arya had brought two sandwiches, one made of vegetables and one of jam. The other two students Abhimanyu and Vivek forgot to bring their lunch today. Arya agreed to share his two sandwiches so that all three would have an equal share of each sandwich.

How can Arya divide his two sandwiches so that each person has an equal share?

Answer 6. He will have to divide each of the sandwiches into three equal parts.

What part of a sandwich will each student receive?

Each boy will receive 1×1/3 or 1/3 sandwiches of each type.

Question 7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Answer 7. Total number of dresses = 30

Number of dresses finished by Kanchan = 20

Fraction of dresses finished = 20/30 or 2/3

Question 8. The two consecutive integers in between which the fraction 5/7 lies are

(A) 5 and 7

(B) 0 and 1

(C) 5 and 6

(D) 6 and 7

(B) 0 and 1

A fraction whose numerator(N) is less than the denominator(D) is called a proper fraction.

So, 5/7 = 0.715

Therefore, 5/7 lies between 0 and 1.

Question 9.

Write down the 11 natural numbers from 2 to 12. What fraction of them are prime numbers?

Natural numbers from 2 to 12 are – 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Prime numbers from among these numbers are 2, 3, 5, 7, and 11.

Therefore, out of the 11 numbers, 5 are prime numbers. It represents a fraction of 5/11.

Question 10.

Write the 12 natural numbers from 102 to 113. What fraction of them are prime numbers?

Natural numbers from 102 to 113 are – 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Among these 12 numbers, the 4 prime numbers are 103, 107, 109, and 113.

Therefore, out of the 12 numbers, 4 are prime numbers. It represents a fraction of 4/12.

Question 11. When ¼ is written with the denominator as 12, its numerator is

(A) 3

(B) 8

(C) 24

(D) 12

(A) 3

(1 × 3)/(4 × 3) = 3/12

Consider, 3/12

Divide both numerator and denominator by 3.

= 1/4

Question 12. Which of the following fraction is not equal to the others?

(i) 6/8

(ii) 12/16

(iii) 15/25

(iv) 18/24

(iii) 15/25

All the options given in the question are further simplified as follows,

(i) 6/8

Divide both numerator and denominator by 2.

= 3/4

(ii) 12/16

Divide both numerator and denominator by 4.

= 3/4

(iii) 15/25

Divide both numerator and denominator by 5.

= 3/5

(iv) 18/24

Divide both numerator and denominator by 6.

= ¾

Comparing all results, (¾ = ¾ = ¾) ≠ 3/5

Therefore, (6/8 = 12/16 = 18/24) ≠ 15/25

Question 13. Which of the following given fractions is the greatest?

(i) 5/7

(ii) 5/6

(iii) 5/9

(iv) 5/8

(ii) 5/6

We know that among all fractions with the same numerator, the one having a smaller denominator will be the highest fraction.

5/9 < 5/8 < 5/7 < 5/6

Therefore, among four options, (ii) 5/6 has a small denominator. So, it is the greatest fraction.

Question 14. The mixed fraction 5(4/7) can also be expressed as –

(i) 33/7

(ii)39/7

(iii) 33/4

(iv) 39/4

(ii) 39/7

The mixed fraction 5(4/7) can be expressed as = 5 + (4/7)

= (35 + 4)/7

= 39/7

Question 15. Is 7/19 a fraction?

7/19 is a proper fraction.

A fraction whose numerator(N) is less than the denominator(D) is called a proper fraction.

Question 16. Are 5/8 and 3/8 proper fractions or not?

5/8 and 3/8 are like proper fractions.

Fractions with the same denominators are called fractions.

Question 17. What type of fractions are 18/135 and 90/675. Are they proper, unlike fractions?

18/135 and 90/675 are proper, unlike and equivalent fractions.

Consider the two given fractions, 18/135 and 90/675

So, (18/135) = (90/675)

By cross multiplication, we get

(18 × 675) = (90 × 135)

12,150 = 12,150

Therefore, 18/135 and 90/675 are proper, unlike and equivalent fractions.

Question 18. The following fractions below are represented by just three different numbers. Now, separate them into three groups of all equivalent fractions by changing each one of them to its simplest form.

(i) 2/12 (ii) 3/15 (iii) 8/50 (iv) 16/100 (v) 10/60 (vi) 15/75

(vii) 12/60 (viii) 16 / 96 (ix) 12 / 75 (x) 12 / 72 (xi) 3 / 18 (xii) 4/25

(i) 2 / 12 = (1 × 2) / (6 × 2)

= 1 / 6

(ii) 3 / 15 = (1 × 3) / (5 × 3)

= 1 / 5

(iii) 8 / 50 = (4 × 2) / (25 × 2)

= 4 / 25

(iv) 16 / 100 = (4 × 4) / (25 × 4)

= 4 / 25

(v) 10 / 60 = (1 × 10) / (6 × 10)

= 1 / 6

(vi) 15 / 75 = (1 × 15) / (5 × 15)

= 1 / 5

(vii) 12 / 60 = (1 × 12) / (5 × 12)

= 1 / 5

(viii) 16 / 96

= (1 × 16) / (6 × 16)

= 1 / 6

(ix) 12 / 75 = (4 × 3) / (25 × 3)

= 4 / 25

(x) 12 / 72 = (1 × 12) / 6 × 12)

= 1 / 6

(xi) 3 / 18 = (1 × 3) / (6 × 3)

= 1 / 6

(xii) 4 / 25

Totally there are three groups of equivalent fractions.

1 / 6 = (a), (e), (h), (j), (k)

1 / 5 = (b), (f), (g)

4 / 25 = (c), (d), (i), (l)

Question 19. Find the answers to the following. Write and indicate how to solve the following:

(a) Is 5 / 9 equals(=) to 4 / 5

(b) Is 9 / 16 equals(=) to 5 / 9

(c) Is 4 /5 equals(=) to 16 / 20

(d) Is 1 / 15 equals(=) to 4 / 30

(a) 5 / 9 and 4 / 5

Now, convert all these fractions into like fractions:

5 / 9 = (5 / 9) × (5 / 5)

= 25 / 45

4 / 5 = (4 / 5) × (9 / 9)

= 36 / 45

∴ 25 / 45 ≠ 36 / 45

Therefore, 5 / 9 is not equal to 4 / 5

(b) 9 / 16, 5 / 9

Convert all these fractions into like fractions:

9 / 16 = (9 / 16) × (9 / 9)

= 81 / 144

5 / 9 = (5 / 9) × (16 / 16)

= 80 / 144

∴ 81 / 144 ≠ 80 / 144

Therefore, 9 / 16 is not equal to 5 / 9

(c) 4 / 5, 16 / 20

16 / 20 = (4 × 4) / (5 × 4)

= 4 / 5

∴ 4 / 5 = 16 / 20

Therefore, 4 / 5 is equal to 16 / 20

(d) 1 / 15, 4 / 30

4 / 30 = (2 × 2) / (15 × 2)

= 2 / 15

∴ 1 / 15 ≠ 4 / 30

Therefore, 1 / 15 is not equal to 4 / 30.

Question 20. Rafiq had exercised for 3 / 6 of an hour today, while Rohit exercised for 3 / 4 of an hour today. Who exercised for a longer ime today?

Rafiq exercised = 3 / 6 of an hour

Rohit exercised = 3 / 4 of an hour.

3 / 6 and 3 / 4

Convert both of these into like fractions:

(1) 3 / 6 = (3 × 2) / (6 × 2) = 6 / 12

(2) 3 / 4 = (3 × 3) / (4 × 3) = 9 / 12

So clearly, 9 / 12 is greater than 6 / 12.

∴ 3 / 4 > 3 / 6

Hence, Rohit exercised for a longer time than Rafiq.

Question 21. In class A of total 25 students, 20 passed with 60% or more marks; in class B, of total 30 students, 24 passed with 60% or re marks. Calculate in which class was a greater fraction of students getting 60% or more marks.

The total number of students in Class A = 25

Students passed in the first class in Class A = 20

Therefore, fraction = 20 / 25

= 4 / 5

The total number of students in Class B = 30

Students passed in the first class in Class B = 24

Therefore, fraction = 24 / 30

= 4 / 5

∴ An equal fraction of the students passed in first class in both classes

Question 22.

Write all these fractions appropriately as additions or subtractions:

(a) The total number of parts each rectangle has = 5

No. of all shaded parts in first rectangle = 1 i.e 1 / 5

No. of all shaded parts in second rectangle = 2 i.e 2 / 5

No. of all shaded parts in third rectangle = 3, i.e. 3 / 5

Clearly, the fraction which is represented by the third rectangle = the sum of the fractions represented by the first and the second rectangle.

Therefore, 1 / 5 + 2 / 5 = 3 / 5

(b) The total number of all parts each circle has is = 5

We have observed that the first, second and third circles represent 5, 3 and 2 shaded parts out of total 5 equal parts, respectively. Clearly, the Fraction represented above by the third circle is the difference between the fractions represented by the first and second circles.

Hence, 5 / 5 – 3 / 5 = 2 / 5

(c) Here, we may observe that the first, second and third rectangles represent 2, 3 and 5 shaded parts out of 6 equal parts, respectively. Clearly, the fraction represented by the third rectangle is the sum of fractions represented by the first and second rectangles.

Hence, 2 / 6 + 3 / 6 = 5 / 6

Question 23.

Answer 23. Total number of CDs with Kristin = 3 + 5

= 8

Total number of CDs she bought = 3

fraction of CDs she bought = 3/8

Question 24.

Ramesh had 20 pencils, whereas Sheelu had 50 pencils, and Jamaal had 80 pencils. After four months, Ramesh used up ten pencils, Sheelu also used up 25 pencils, and Jamaal also used up 40 pencils. What fraction did each of them use up? Check if each of them has used up an equal fraction of her/his pencils.

Fraction used by Ramesh = 10/20 =1/2

Fraction used by Sheelu = 25/50 = 1/2

Fraction used by Jamaal = 40/80 = 1/2

Yes, all of them used an equal fraction of pencils, i.e., 1/2.

Question 25.

Write the fractions and pair up with the equivalent fractions from each row.

(a) Here, 1 part is shaded out of total of 2 equal parts (i.e., rectangle). Hence, this figure represents a fraction 1/2.

(b) Here, four parts are shaded out of 6 equal parts (i.e., rectangle). Hence, this figure represents a fraction of 4/6 = 2/3.

(c) Here, three parts are shaded out of 9 equal parts (i.e., squares). Hence, this figure represents a fraction of 3/9 = 1/3.

(d) Here, two parts are shaded out of 8 equal parts (i.e., rectangle). Hence, this figure represents a fraction of 2/8 = 1/4.

(e) Here, three parts are shaded out of 4 equal parts (i.e., squares). Hence, this figure represents a fraction of 3/4.

(i) Here, six parts are shaded out of 18 equal parts (i.e., triangles). Hence, this figure represents a fraction of 6/18 = 1/3.

(ii) Here, four parts are shaded out of 8 equal parts (i.e., rectangles). Hence, this figure represents a fraction of 4/8 = 1/2.

(iii) Here, 12 parts are shaded out of total of 16 equal parts (i.e., squares). Hence, this figure represents a fraction of 12/16 = 3/4.

(iv) Here, eight parts are shaded out of 12 equal parts (i.e., rectangles). Hence, this figure represents a fraction of 8/12 = 2/3.

(v) Here, four parts are shaded out of 16 equal parts (i.e., triangles). Hence, this figure represents a fraction of 4/16 = 1/4.

Now, these figures above can be matched correctly as

(a)-(ii), (b)-(iv), (c)-(i), (d)-(v), (e)-(iii)

Question 26.

Fill in the blanks:

There is a large box of 36 small square boxes.

1. 1/2 of it is _____.
2. 2/3 of it is _____.
3. If I make a bench of 20 small boxes, the fraction becomes _____.
4. _____ boxes are required if the fraction is ⅚.

1. ½ of 36 is equal to 18
2. = 1/2 of 36 boxes

= 1/2× 36

= 36/2 = 18 boxes.

2/3rd of 36 is equal to 24

1. If a bench is made with 20 boxes out of 36 boxes, the fraction becomes 5/9.

20/36

20÷4/36÷4

5/9

So, if i make a bench of 20 small boxes, the fraction becomes 5/9

1. __boxes are required for the fraction to be 5/6.

⅚ = x/36

x = (36×5)÷6

x = 30

So, 30 boxes are required for the fraction to be 5/6

Question 27. Solve:

(a) 1 / 18 + 1 / 18

(b) 8 / 15 + 3 / 15

(c) 7 / 7 – 5 / 7

(d) 1 / 22 + 21 / 22

(e) 12 / 15 – 7 / 15

(f) 5 / 8 + 3 / 8

(g) 1 – 2 / 3 (1 = 3 / 3)

(h) 1 / 4 + 0 / 4

(i) 3 – 12 / 5

(a) 1 / 18 + 1 / 18

= (1 + 1) / 18

= 2 / 18

= 1 / 9

(b) 8 / 15 + 3 / 15

= (8 + 3) / 15

= 11 / 15

(c) 7 / 7 – 5 / 7

= (7 – 5) / 7

= 2 / 7

(d) 1 / 22 + 21 / 22

= (1 + 21) / 22

= 22 / 22

= 1

(e) 12 /15 – 7 / 15

= (12 – 7) / 15

= 5 / 15

= 1 / 3

(f) 5 / 8 + 3 / 8

= (5 + 3) / 8

= 8 / 8

= 1

(g) 1 – 2 / 3

= 3 / 3 – 2 / 3

= (3 – 2) / 3

= 1 / 3

(h) 1 / 4 + 0

= 1/ 4

(i) 3 – 12 / 5

= 15 / 5 – 12/ 5

= (15 – 12) / 5

= 3 / 5

Question 28. Shubham had painted 2 / 3 of the wall space in his room. His sister Madhavi had helped and painted 1 / 3 of the wall space. How much did they paint together?

Wall space painted by Shubham in a room = 2 / 3

Wall space painted by Madhavi in a room = 1 / 3

Total space painted by both = (2 / 3 + 1 / 3)

= (2 + 1) / 3

= 3 / 3

= 1

∴ Shubham and Madhavi together painted one complete wall in a room.

Question 29. Nandini’s house is about 9 / 10 km from her school. She walked some distance towards her school and then took a bus for 1 / 2 km to reach the school. How far did she walk?

Distance of the school from house = 9 / 10 km

The distance she travelled by bus = 1 / 2 km.

Distance walked by Nandini = Total distance of the school – Distance she travelled by bus.

= 9 / 10 – 1 / 2

= [(9 × 1) – (1 × 5)] / 10

= (9 – 5) / 10

= 4 / 10

= 2 / 5 km

∴ The distance walked by Nandini is 2 / 5 km.

Question 30. Asha and Samuel had bookshelves of the same size, partly filled with books. Asha’s shelf is 5 / 6th full, and Samuel’s shelf is 2/ 5 th full. Whose bookshelf is more full? By what fraction?

Fraction of Asha’s bookshelf = 5 / 6

Fraction of Samuel’s bookshelf = 2 / 5

Convert these fractions into like fractions

5 / 6 = 5 / 6 × 5 / 5

= (5 × 5) / (6 × 5)

= 25 / 30

2 / 5 = 2 / 5 × 6 / 6

= (2 × 6) / (5 × 6)

= 12 / 30

25 / 30 > 12 / 30

5 / 6 > 2 / 5

∴ Asha’s bookshelf is little more full than Samuel’s bookshelf.

Difference = 5 / 6 – 2 / 5

= 25 / 30 – 12 / 30

= 13 / 30

Question 31. Jaidev takes around minutes to walk across the school ground. Rahul takes around 7 / 4 minutes to do the same. Who takes lesser time, and by what fraction?

Time is taken by Jaidev to walk across the school ground =

= 11 / 5 minutes

The time it took for Rahul to walk across the school ground = was 7 / 4 minutes.

Convert these fractions into like fractions

11 / 5 = 11 / 5 × 4 / 4

= (11 × 4) / (5 × 4)

= 44 / 20

7 / 4 = 7 / 4 × 5 / 5

= (7 × 5) / (4 × 5)

= 35 / 20

Clearly, 44 / 20 > 35 / 20

11 / 5 > 7 / 4

∴ Rahul takes lesser time than Jaidev to walk across the school ground.

Difference = 11 / 5 – 7 / 4

= 44 / 20 – 35 / 20

= 9 / 20

Hence, Rahul walks across the school ground for 9 / 20 minutes.

Question 32. A small piece of wire 7 / 8 metre long broke into two pieces. One piece is 1 / 4 metre long. How long is the other piece?

Total length of the wire = 7 / 8 metre

Length of one piece of the wire = 1 / 4 metre

Length of another piece of the wire = Length of the original wire, and this one piece of wire

= 7 / 8 – 1 / 4

= [(7 × 1) – (1 × 2)] / 8

= (7 – 2) / 8

= 5 / 8

∴ Length of the other piece of the wire = 5 / 8 metre

Question 33. Sarita bought 2 / 5 metres of ribbon and Lalita 3 /4 metres of the ribbon. What is the total length of the ribbon that they bought?

Length of the ribbon bought by Sarita = 2 / 5 metre

Length of the ribbon bought by Lalita = 3 / 4 metre

Total length of the ribbon bought by two of them = 2 / 5 + 3 / 4

Taking LCM 20

= [(2 × 4) + (3 × 5)] / 20

= (8 + 15) / 20

= 23 / 20 metre

∴ The total length of the ribbon that was bought by both Sarita and Lalita is 23 / 20 metres.

### Benefits of Solving Important Questions Class 6 Maths Chapter 7

One must practise scoring better marks in exams. The more one can practise, the better one can do in Maths. So, students must build the habit of solving questions from each chapter. It will help them clear their understanding of each concept and increase their confidence. Moreover, it will help them to score better in exams. There will be other benefits of solving the Important Questions Class 6 Maths Chapter 7. They are-

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Extramarks understands the needs of students. We provide a wide range of study materials to help students score better marks in exams. You can register on our official website to avail the study materials. You will find the CBSE syllabus, NCERT books, NCERT solutions, CBSE revision notes, CBSE extra questions, CBSE sample papers, CBSE past years’ question papers, NCERT important questions, vital formulas and many more. Like the Important Questions Class 6 Maths Chapter 7, you can also find important questions for other chapters of Class 6 Maths. The following links to the study materials are given here.

Q.1 In the following figures, the figure that is representing the fraction 3/5 of the shaded region to the unshaded region is   (i)

(ii)

(iii)

(i) and (iii) both

Marks:1

Ans

(i)

So, figure (i) is the correct figure.

Q.2 Which of the following fractions is written in the simplest form            Marks:1

Ans Q.3 Which of the following fractions is the greatest

A. B. C. D. Marks:1

Ans  Q.4 Arrange the following in descending order.

$\left(\mathrm{i}\right)\text{}\frac{4}{6},\frac{5}{8},\frac{7}{12},\frac{5}{16}\text{}\left(\mathrm{ii}\right)\text{}\frac{8}{17},\frac{8}{9},\frac{8}{5},\frac{8}{13}$

Marks:4

Ans

$\begin{array}{l}\left(\mathrm{i}\right)\text{}\frac{4}{6},\frac{5}{8},\frac{7}{12},\frac{5}{16}\\ \mathrm{LCM}\text{of 6, 8, 12 and 16}\\ 2\overline{)\text{6, 8, 12, 16}}\\ 2\overline{)\text{3, 4, 6, 8}}\text{}\\ 2\overline{)\text{3, 2, 3, 4}}\\ 2\overline{)\text{3, 1, 3, 2}}\\ 3\overline{)\text{3, 1, 3, 1}}\\ \text{}\overline{)\text{1, 1, 1, 1}}\\ \end{array}$ $\begin{array}{l}\mathrm{LCM}\text{of 6, 8, 12 and 16}=2—2—2—2—3\\ \text{}=48\\ \mathrm{So},\text{}\frac{4}{6},\frac{7}{12},\frac{5}{8},\frac{5}{16}=\frac{4—8}{6—8},\frac{7—4}{12—4},\frac{5—6}{8—6},\frac{5—3}{16—3}\\ \text{}=\frac{32}{48},\frac{28}{48},\frac{30}{48},\frac{15}{48}\\ \mathrm{Descending}\text{order is:}\\ \frac{32}{48},\frac{30}{48},\frac{28}{48},\frac{15}{48}=\frac{4}{6},\frac{5}{8},\frac{7}{12},\frac{5}{16}\end{array}$

$\begin{array}{l}\left(\mathrm{ii}\right)\text{}\frac{8}{17},\frac{8}{9},\frac{8}{5},\frac{8}{13}\\ \mathrm{Since},\text{two fractions with same}\\ \text{numerators are compared, the fraction}\\ \text{with the greater denominator will be}\\ \text{the er fraction.}\\ \text{So, the ascending order of denominators is}\\ 5<\text{9< 13< 17}\\ \text{Thus, descending order of fractions is}\\ \frac{8}{5}>\frac{8}{9}>\frac{8}{13}>\frac{8}{17}\end{array}$

Q.5 Find the equivalent fraction of

$\frac{5}{9}$

with denominator 63.

Marks:1

Ans

$\frac{5}{9}=\frac{5—7}{9—7}=\frac{35}{63}$