Class 6 Mathematics Chapter 7 Solution (English Medium) – Fractions | SCERT Assam

SCERT Assam Class 6 Mathematics Chapter 7 – “Fractions” Summary & Solutions

SCERT Assam Class 6 Mathematics (English Medium) Chapter 7 – “Fractions” solutions are available at Ospin Academy. We provide SCERT-based textbook solutions, multiple-choice questions (MCQs), and a complete chapter summary to help students in their exam preparation.

📖 Chapter Overview:

This chapter introduces **fractions**, their types, and how to perform different operations on them.

• Types of Fractions: Proper, improper, mixed fractions.
• Operations on Fractions: Addition, subtraction, multiplication, and division.
• Comparison of Fractions: Finding greater and smaller fractions.

📌 Exercises Covered in Lesson 7:

• Exercise 7A: Identifying and classifying fractions.
• Exercise 7B: Addition and subtraction of fractions.
• Exercise 7C: Multiplication and division of fractions.
• Exercise 7D: Comparing and simplifying fractions.
• Exercise 7E: Word problems based on fractions.

📝 Ospin Academy Resources:

• Complete Solutions: SCERT Assam Class 6 Mathematics Chapter 7 answers.
• MCQs & Additional Questions: Exam-focused multiple-choice questions.
• Clear Explanations: Concepts explained in simple terms.
• Quick Revision Notes: Concise notes for last-minute preparation.

For SCERT Assam Class 6 Mathematics (English Medium) Chapter 7 – “Fractions” solutions, visit Ospin Academy.

Class 6 Mathematics

• Chapter – 7 (Ospin Academy)

Fractions

Exercise – 7 (A)

Q 1. Write the fraction representing the shaded portion.

Ans: (i) 4 / 16

(ii) 3 / 16

(iii) 8 / 15

(iv) 6 / 8

Q 2. Write whether the fraction identifying the shaded portion is correct or not.

(i)

Ans: Incorrect.

(ii)

Ans: Correct.

Q.3. Shade 7 parts of the adjacent ring. Write the fraction representing the shaded portion.

Ans: 7/16

Q.4. Write the natural numbers from 1 to 50. Encircle the prime numbers from them. What fraction of the natural numbers are prime numbers, express them.

Ans: The natural numbers from 1 to 50:

Total Numbers = 50

Total Prime numbers = 15

∴ 15/50 of the natural numbers are prime numbers.

Q. 5. What fraction of a year is 5 months.

Ans: 1 year = 12 months.

∴ fraction of a year is 5 months = 5/12

6. Write the proper fractions whose-

(a) Denominator is 11.

Ans: 7 /11

(b) Numerator is an even prime number and denominator is 3 more than that.

Ans: 5 / 2.

7. (a) Write a proper fraction whose, sum of denominator and numerator is 9. Is there any more proper fraction satisfying this condition? Match the fractions which you got, with the fractions, which your class – mate found out.

Ans: According to given condition, the proper fraction is 4/5. Such proper fraction are 1/3, 2 / 7,3 / 6,etc.

(b) Write a proper fraction, whose numerator is 3 less than the denominator Can you write 5 more fractions of this type? Can you think, how many such fraction are there?

Ans: Five proper fraction and whose numeration is 3 less than the denominator are 1/4, 2/5, 3/6 ,4/7 and 5/8.

Those are many such fractions.

Q.8. Write a fraction whose numerator is 7 more than the denominator. Is it proper or improper fraction? Can you write 5 more fractions of this type?

Ans: 9 / 2[2 + 7 = 9], this is an improper fraction

5 more fractions of this type are- 10 / 3, 11 / 4, 12 / 5, 13 / 6, 15 / 8.

Q.9. How can you share 5 apples among 3 students? Express the quantity received by each student in mixed fraction.

Ans: Out of 5 apples, 3 apples can be distributed among 3 students. The 4th and 5th apples can also be distributed among 3 students, thus each student receives (1 + ⅓ + 1 / 3) = (1 + 2 / 3) = 1 2 / 3 apples.

Q.10. How can you share 7 apples among 2 girls, (Use both the ways used earlier).

Ans: Let us suppose, 7 apples will be shared between 2 girls. Out of 7 apples, 6 apples are shared between 2 girls. The 7th apple is divided into two parts and shared by giving half of an apple to each of them.

Hence, the portion of the first girl is (3 + 1/2) of the apple

and that of the second girl is (3 + 1/2) of the apple.

Again, this can be done by another other way also.

Exercise – 7(B)

1. Draw a number line and locate 1 / 4, 2 / 4, 3 / 4, 4 / 4.

Ans: Location of 1 / 4, 2 / 4, 3 / 4, 4 / 4 on a number line:

2. Where to locate 0/10, 3/10, 7/10 and 10/10 on the number line?

Ans: Location of 0 / 10, 3 / 10, 7 / 10 and 10 / 10 on the number line:

3. Draw number line and locate the following-

(a) 4/9

Ans:

(b) 4 ⅔

Ans:

(c) 11/3

Ans: 11/3 = 3 2\3

Q.4. (i) When a fraction will become equal to 1?

Ans: When the value of the numerator and the denominator of a fraction is equal, then a fraction becomes equal to 1.

(ii) When a fraction will become less than 1?

Ans: When the value of numerator is less than the value of denominator, then a fraction becomes less them 1.

Q.5. Write 5 improper fractions whose denominators are greater than 10.

Ans: 13/11,14/11,15/11,16/11,17/11.

6. Write three mixed fractions. The mixed fractions as improper fractions.

Ans:

Improper fractions of the above three mixed fractions are 13/5, 23/7 and 27/4.

7. Suppose 22/5 indicates that 22 fruits are to be shared among 5 persons equally. Express this sharing by using diagrams. How many whole fruits will be shared among them? After getting a whole fruit each, how many parts will each of them get?

Ans: When 22 fruits are shared among persons, the each person gets 22/5 = 4 2/5 parts.

∴ Each person gets 4 whole fruits and ⅖ part.

8. Draw four circles of equal size. Show that 1/2, 2/4, 4/8 and 8/16 are equivalent fractions and that, they represent the same shared part of a whole and explain.

Ans:

9. Draw three dials of a clock of equal size as shown in the adjacent figure. Represent the fractions 3/4 ,5/6 and 7/12 on them and try to explain that they do not represent the same part of the dials.

Ans:

Exercise – 7 (C)

Q.1. Find four equivalent fractions of 2/9.

Ans:

Q.2. Find three equivalent fractions of ⅜ (Can you represent them with the help

of pictures that they are equivalent)?

Ans:

Q. 3. Observe the adjoining figures. Write the fraction of the shaded parts in each of them. Are all these fraction equivalent?

Ans: (i) 15 / 25 = 3/5

∴ 15 x 5 = 75

25 x 3 = 75

(ii) 4 / 9 = 36 / 81

∴ 4 x 81 = 324

9 x 36 = 324

Q. 2. Fill in the—

(a)

Ans:

(b)

Ans:

(c)

Ans:

5. (a) Find the equivalent fractions of 5 / 8 having

(i) denominator 40

Ans: denominator = 40

(ii) denominator 6 more than the numerator.

Ans: Let the denominator be x + 6

5/8 = x / x + 6

5(x + 6) = 8x

5x + 30 = 8x

30 = 8x – 5x

30=3x

10 = x

 

the numerator is 10, and the denominator is: 10 + 6

= 16

the required fraction is: 10 / 16.

(b) Multiply both the numerator and denominator of 5/8 by 2, 3, 4, 5, 6 respectively and find the equivalent fractions accordingly. Find the difference between the denominator and numerator of each of the fractions and write them serially. Doing so, have you find any pattern in them,mention.

Ans:

Q.6. Check whether each pair of fractions are equivalent.

(i) 3 / 10, 15 / 50

Ans:

(ii) 7/9, 42/72

Ans:

7. (a) Reduce the following fractions to the lowest form (dividing by the HCF of numerator and denominator in each case)

(i) 45 / 60.

Ans: 45 / 60

45 = 3 x 3 x 5

60 = 2 x 2 x 3 x (5)

∴ H.C.F = 3 x 5 = 15.

(ii) 90/150

Ans: 90 / 150

90 = 2 x 3 x 3 x 5

150 = 2 x 3 x 5 x 5

∴ H.C.F = 2 x 3 x 5 = 30

(iii) 48/72

Ans: 48 / 72

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

∴ H.C.F. = 2 x 2 x 2 x 3 x 3 = 24

(b) Reduce the following fractions to the lowest form by prime factorising the numerator and denominator in each case.

(i) 105 / 195

Ans:

(ii) 72 / 104

Ans:

Exercise – 7(D)

1. (i) How will you find, which one is the larger fraction between 15/20 and 13/20.

Ans: In the given fractions, denominators are equal and 15 > 13

∴ 15 / 20 > 13/20

(ii) Write the fractions 3 /16, 19/16, 8/16, 9/16, 13/16, 5/16 in descending order.

Ans:

(iii) Which fraction is the biggest among 1/6, 1/2, 1/9.

Ans:

∴ The biggest fraction = ½.

2. Find which of the following pairs of fractions is like fraction.

(a) 6/11, 2/11.

(b) 11 2/4,11 ⅗.

(c) 5/9, 5/11.

(d) 5/6, 6/5

Ans: Like pair of fractions: (a) 6 / 11, 2 / 11

3. Find which one of each pair of fractions is greater.

(a) 3/4, 2/5

Ans:

 

(b) 4 3/5, 5 2/7

Ans:

(c) 8 2/7, 8 3/8

Ans:

4. Convert them to their lowest form and then compare them.

(i) 10/15, 25/75

Ans:

(ii) 40/64, 96/120

Ans:

5. Find which one of each pair of fractions is smaller(with the help of the diagrams).

(a) 3/4, 2/6

Ans:

(b) 3/3, 3/7

Ans:

(c) 3/5, 2/3

Ans:

6. (a) Arrange the fractions in descending order.

(i) 3/8, 9 /16, 19 / 24 ,1/4.

Ans:

(ii) 3 / 2 ,11 / 18, 22 / 27,7 / 9.

Ans:

(b) Arrange the fractions in ascending order.

(i) 3 / 10, 13 / 15,6 / 7,⅘.

Ans:

(ii) 10/21, 31/42, 13/14, 5/7.

Ans:

7. From two different High Schools, the number of students who appeared for the HSLC examination are 80 and 90 respectively. 60 students from the first school and 72 from the second were successful by securing first division. From which school, did the highest number of students pass in first division?

Ans: Number of students from the 1st School secured 1st division = 60

and from the 2nd School secured 1st division = 72

Exercise – 7 (E)

Q.1. Fill in the blank spaces by observing the pictures aside.

Ans:

Q.2. To get 19/24 – 13/24 = 6/24 draw some circles like above and explain the steps.

Ans:

Q.3. Find the value of-

(i) 3/17 + 4/17 + 6/17

Ans:

(ii) 9/26 + 13/26

Ans:

(iii) 29/51 + 31/51

Ans:

Ans:

(v) 14 / 25 – 11 / 25.

Ans:

(vi) 1- 31 / 35.

Ans:

(vii) 4 – 14 / 4.

Ans:

Q 4. Add the following:

(a) 3/4 + 4/3

Ans:

(b) 1 + 3/5

Ans:

(c) 5 + 1/7

Ans:

(d) 2/3 + 1/4 + 1/2

Ans:

Ans:

Ans:

Ans:

5. Subtract the following:

Ans:

Ans:

Ans:

Ans:

Q. 6. Simplify-

Ans:

Ans:

Ans:

Q.7. Priti and Riti’s mother kept the glass of milk on the table. She asked them to share the glass of milk. Priti took 2/4 parts of the milk and Riti took 1/2 part. How much milk was left in the glass?

Ans: Priti took milk from the glass full of milk = 2/4 part

and Riti took milk = ½ Part.

∵ Priti and Riti took milk together =

∴ Amount of milk was left in the glass = 1-1 = 0

∴. No milk was left in the glass.

Q.8. From an exercise, 5/19 parts of the sums were solved by the class teacher. The students themselves solved 3/19 part of the sums.What part of the exercise are left to solve?

Ans: The sums are solved by the class teacher = 5 / 19 parts.

and sums are solved by the students = 3 / 19 parts.

Q.9. From one litre of milk Nabamallika’s mother gave 1/5 parts to Nabamallika and 2/9 parts to Madhumalati to drink. How many parts in total from one litre of milk was taken by both of them?

Ans: From 1 litre of milk Nabamallika’s mother gave 1/5 parts to

Nabamallika and 2/9 parts to Madhumalati.

Q.10. From a bucket full of water, 7/15 parts of water was used. How much water was left in the bucket?

Ans: From a bucket full of water, 7/15 parts of water was used.

Amount of water left in a bucket = (1 – 7 / 15)

= 15 -7/15 parts

= 8/15 parts.

Q.11. Ranu’s school is 7/8 km away from her house. Daily she walks a distance and then takes a bus to travel 5/8 km to reach the school. How far does she walk? Why does she walk for some distance daily?

Ans: Ranu’s school is 7/8 km away from her house.

She takes a bus for 5/8 km

Distance Walked =Total Distance−Bus Distance

= 7/8 – 5/8

= 7 – 5/8

= 2/8

= 1/4

Ranu walks 1/4 km daily before taking the bus.

12. Birina’s friends take 5/9 parts of olives which were with her. How many parts are now left with her?

Ans: Birina’s friends takės 5 / 9 Parts of olives which was with her.

13. If 5/8 is subtracted from a number, the difference becomes 1/4 What is the number?

Ans:

14. Robin went to the town with his father to sit for a competitive examination. Robin and his father start their journey from home and travelled 1/12 parts of the distance by bicycle, after that they went by bus and lastly 1/20 parts they went on foot. How many parts of the distance did they move by?

Ans: Robin and his father travelled 1/12 parts of the distance by bicycle, after that they went by bus.

Lastly 1/20 parts they went on foot.

Total parts travelled by bicycle and on foot = 1/12 + 1/20

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