Class 6 Maths - Fractions NCERT Solutions

Chapter 7: Fractions (NCERT Solutions)

Exercise 7.1 (Introduction to Fractions)

Q1. Write the fraction representing the shaded portion.
(i) 4 shaded out of 9 equal parts (ii) 6 shaded out of 12 equal parts

(i) Fraction = 4/9

(ii) Fraction = 6/12 = 1/2

Q2. Find the fraction of coloured region: (a) 2 of 6 parts coloured (b) 3 of 8 parts coloured

(a) 2/6 = 1/3

(b) 3/8

Q3. Shade the following fractions in the given boxes:
(a) 3/4 (b) 1/6 (c) 4/9

(a) Divide into 4 equal parts; shade 3 parts.

(b) Divide into 6 equal parts; shade 1 part.

Q5. A fraction has numerator 3 and denominator 5. Write it. What does the numerator and denominator represent?

Fraction = 3/5.
Numerator (3): The number of equal parts taken.
Denominator (5): The total number of equal parts the whole is divided into.

Q8. What fraction of a day is 8 hours?

Total hours in a day = 24.
Fraction = 8/24 = 1/3 of a day.

Q9. What fraction of an hour is 40 minutes?

Total minutes in an hour = 60.
Fraction = 40/60 = 2/3 of an hour.

Exercise 7.2 (Proper, Improper & Mixed Fractions)

Q1. Draw number lines and locate the points:

On a number line, fractions between 0 and 1 are located by dividing the unit into equal parts equal to the denominator. For example, 1/4 is 1 part out of 4 equal parts between 0 and 1.

Q2. Express as mixed fractions:
(a) 17/3 (b) 11/4 (c) 17/5 (d) 28/5 (e) 19/6 (f) 35/9

(a) 17 ÷ 3 = 5 rem 2 → 5 and 2/3

(b) 11 ÷ 4 = 2 rem 3 → 2 and 3/4

(d) 28 ÷ 5 = 5 rem 3 → 5 and 3/5

(e) 19 ÷ 6 = 3 rem 1 → 3 and 1/6

(f) 35 ÷ 9 = 3 rem 8 → 3 and 8/9

Q3. Express as improper fractions:
(a) 7 and 3/4 (b) 5 and 6/7 (c) 2 and 5/6 (d) 10 and 3/5

Rule: (whole × denominator + numerator) / denominator

(a) (7×4 + 3)/4 = (28+3)/4 = 31/4

(b) (5×7 + 6)/7 = (35+6)/7 = 41/7

(d) (10×5 + 3)/5 = (50+3)/5 = 53/5

Exercise 7.3 (Equivalent Fractions & Simplest Form)

Q1. Write the fractions. Are they equivalent?
(a) 2/3 and 4/6 (b) 3/5 and 6/15

(a) 2/3: multiply numerator and denominator by 2 → 4/6. So 2/3 = 4/6. Yes, equivalent.

(b) 3/5: multiply by 3 → 9/15. But 6/15 ≠ 9/15. Not equivalent.

Q2. Give three equivalent fractions for each of:
(a) 2/3 (b) 1/5 (c) 3/5 (d) 5/9

(a) 2/3 → 4/6, 6/9, 8/12

(b) 1/5 → 2/10, 3/15, 4/20

(d) 5/9 → 10/18, 15/27, 20/36

Q5. Reduce to simplest form:
(a) 48/60 (b) 150/60 (c) 84/98 (d) 12/52

(a) HCF(48, 60) = 12. 48/60 = 4/5

(b) HCF(150, 60) = 30. 150/60 = 5/2

(d) HCF(12, 52) = 4. 12/52 = 3/13

Exercise 7.4 (Comparing Fractions)

Q1. Compare and write with <, > or =:
(a) 1/6 ___ 1/3 (b) 3/4 ___ 2/6 (c) 3/5 ___ 2/3 (d) 1/4 ___ 1/4

(a) 1/6 vs 1/3: LCD = 6. 1/6 vs 2/6. 1 < 2. → 1/6 < 1/3

(b) 3/4 vs 2/6: LCD = 12. 9/12 vs 4/12. 9 > 4. → 3/4 > 2/6

(d) 1/4 = 1/4

Q2. Arrange in ascending order:
(a) 1/3, 3/9, 2/6, 1/6 (b) 3/7, 3/11, 3/5, 3/2

(a) Convert to equivalent fractions with LCD = 18:
1/6 = 3/18, 1/3 = 6/18, 3/9 = 6/18, 2/6 = 6/18.
Ascending: 1/6, 1/3 = 3/9 = 2/6

(b) Same numerator; larger denominator = smaller fraction.
Ascending: 3/11, 3/7, 3/5, 3/2

Exercise 7.5 (Addition & Subtraction of Fractions)

Q1. Write the shaded parts as fractions and add them:
(a) 3/8 + 5/8 (b) 1/9 + 2/9 + 3/9

(a) 3/8 + 5/8 = (3+5)/8 = 8/8 = 1

(b) 1/9 + 2/9 + 3/9 = (1+2+3)/9 = 6/9 = 2/3

Q3. Add and simplify if possible:
(a) 2/3 + 1/7 (b) 3/10 + 7/15 (c) 2 and 3/4 + 5 and 1/4 (d) 9/11 − 4/11

(a) LCD = 21. 14/21 + 3/21 = 17/21

(b) LCD = 30. 9/30 + 14/30 = 23/30. 23/30

(d) (9−4)/11 = 5/11

Q4. Subtract:
(a) 5/8 − 1/8 (b) 1 − 2/3 (c) 1/2 − 3/8 (d) 7/8 − 3/5

(a) (5−1)/8 = 4/8 = 1/2

(b) 3/3 − 2/3 = 1/3

(d) LCD = 40. 35/40 − 24/40 = 11/40

Q6. Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in the basket?

Total = 1 (whole basket).
Fraction left = 1 − 5/7 = 7/7 − 5/7 = 2/7 of the basket.

Q7. Asha and Samuel have bookshelves of the same size. Asha's shelf is 5/6 full and Samuel's is 2/5 full. Whose shelf is more full? What fraction is empty for each?

LCD = 30. Asha: 5/6 = 25/30. Samuel: 2/5 = 12/30.
25/30 > 12/30, so Asha's shelf is more full.

Asha's empty portion = 1 − 5/6 = 1/6.

Samuel's empty portion = 1 − 2/5 = 3/5.

Class 6 Maths - Fractions Practice Questions

Chapter 7: Fractions (Practice Questions)

RD Sharma / HOT Practice

Q1. Convert to an improper fraction: 4 and 2/9

(4 × 9 + 2) / 9 = (36 + 2) / 9 = 38/9.

Q2. Convert to a mixed fraction: 47/8

47 ÷ 8 = 5 rem 7. Answer: 5 and 7/8.

Q3. Reduce to simplest form: 128/160

HCF(128, 160) = 32.
128/160 = (128 ÷ 32)/(160 ÷ 32) = 4/5.

Q4. Find a fraction equivalent to 5/8 with denominator 40.

Multiply numerator and denominator by 5: (5×5)/(8×5) = 25/40.

Q5. Arrange in descending order: 5/8, 7/12, 11/24, 2/3

LCD = 24. Convert:
5/8 = 15/24; 7/12 = 14/24; 11/24 = 11/24; 2/3 = 16/24.
Descending: 16/24 > 15/24 > 14/24 > 11/24.
Answer: 2/3, 5/8, 7/12, 11/24.

Q6. A ribbon is 1 and 5/8 m long. Another is 3/4 m long. What is the total length of both?

Convert: 1 and 5/8 = 13/8.
3/4 = 6/8.
Total = 13/8 + 6/8 = 19/8 = 2 and 3/8 m.

Q7. Rahul ran 3/4 of a km and Rashmi ran 5/6 of a km. Who ran more, and by how much?

LCD = 12. 3/4 = 9/12; 5/6 = 10/12.
10/12 > 9/12, so Rashmi ran more.
Difference = 10/12 − 9/12 = 1/12 km = 1/12 km more.

Q8. A piece of wire is 7/8 m long. How much more wire is needed to make it 1 m long?

Needed = 1 − 7/8 = 8/8 − 7/8 = 1/8 m.

Q9. There are 30 students in a class. 2/5 are girls. How many boys are there?

Girls = (2/5) × 30 = 12.
Boys = 30 − 12 = 18 boys.

Q10. Add: 3 and 1/4 + 2 and 1/3 + 1 and 1/6

Sum of whole numbers = 3 + 2 + 1 = 6.
Sum of fractions: LCD = 12. 1/4 + 1/3 + 1/6 = 3/12 + 4/12 + 2/12 = 9/12 = 3/4.
Total = 6 + 3/4 = 6 and 3/4.

Q11. Find the value of: 5/6 − 2/9 + 1/3

LCD = 18. 15/18 − 4/18 + 6/18 = (15 − 4 + 6)/18 = 17/18. 17/18.

Q12. What fraction of a kilogram is 350 grams?

1 kg = 1000 g. Fraction = 350/1000 = 35/100 = 7/20. Answer: 7/20.

Q13. Which fraction is greater: 7/11 or 6/10?

Cross-multiply: 7 × 10 = 70 and 6 × 11 = 66.
70 > 66, so 7/11 > 6/10.

Q14. Write 5 fractions between 1/4 and 1/2.

Convert to equivalent fractions with large denominator: 1/4 = 2/8, 1/2 = 4/8. Need a larger denominator.
With denominator 16: 1/4 = 4/16, 1/2 = 8/16.
Fractions between = 5/16, 6/16, 7/16 and with denominator 20: 1/4 = 5/20, 1/2 = 10/20. Fractions: 6/20 (= 3/10), 7/20, 8/20 (= 2/5), 9/20.

Q15. A water tank is 3/5 full. After using some water, it becomes 2/9 full. What fraction of water was used?

Fraction used = 3/5 − 2/9. LCD = 45.
= 27/45 − 10/45 = 17/45. 17/45 of the tank was used.

Q16. Subtract: 7 and 1/3 − 4 and 2/3

Convert: 7 and 1/3 = 22/3; 4 and 2/3 = 14/3.
22/3 − 14/3 = 8/3 = 2 and 2/3.

Q17. Vikram spent 1/3 of his pocket money on books and 2/5 on stationery. What fraction was spent in total? What fraction is left?

LCD = 15. 1/3 = 5/15; 2/5 = 6/15.
Total spent = 5/15 + 6/15 = 11/15.
Remaining = 1 − 11/15 = 4/15. 11/15 spent; 4/15 left.

Q18. The product of two fractions is 9/16. If one fraction is 3/4, find the other.

Other fraction = (9/16) ÷ (3/4) = (9/16) × (4/3) = 36/48 = 3/4.

Q19. A class has 42 students. 3/7 of them play cricket. How many play cricket and how many do not?

Play cricket = (3/7) × 42 = 3 × 6 = 18 students.
Do not play = 42 − 18 = 24 students.

Q20. Ram ate 3/8 of a pizza and his friend Shyam ate 1/4. What fraction of the pizza is remaining?

Eaten = 3/8 + 1/4 = 3/8 + 2/8 = 5/8.
Remaining = 1 − 5/8 = 3/8 of the pizza.

Class 6 Maths - Fractions Summary

Chapter 7: Fractions (Concepts & Summary)

1. Types of Fractions

Type	Definition	Example
Proper	Numerator < Denominator	3/7, 1/2
Improper	Numerator ≥ Denominator	8/5, 11/3
Mixed	Whole number + Proper fraction	2 and 3/4
Like	Same denominator	1/5, 3/5, 4/5
Unlike	Different denominators	1/3, 1/4, 1/5
Unit	Numerator = 1	1/2, 1/7

2. Equivalent Fractions & Simplest Form

Equivalent fractions represent the same part of a whole. Generated by multiplying or dividing numerator and denominator by the same non-zero number.
e.g., 2/3 = 4/6 = 6/9 = 8/12.
Simplest form: When HCF of numerator and denominator = 1. Divide both by HCF to simplify.
e.g., 24/36 → HCF = 12 → 2/3 (simplest form).

3. Converting Fractions

Mixed → Improper: (Whole × Denominator + Numerator) / Denominator
e.g., 3 and 2/5 = (3×5 + 2)/5 = 17/5

Improper → Mixed: Divide numerator by denominator; quotient is whole number, remainder is new numerator.
e.g., 22/7 = 3 rem 1 = 3 and 1/7

4. Comparing Fractions

Like fractions: Compare numerators directly. Larger numerator = larger fraction.
Unlike fractions: Convert to like fractions using LCD, then compare.
Same numerator: Larger denominator = smaller fraction. (e.g., 1/3 < 1/2)
Cross multiplication: a/b vs c/d → compare a×d and b×c.

5. Addition & Subtraction

Like fractions: Add/subtract numerators directly. Keep denominator same.
3/7 + 2/7 = 5/7 8/9 − 3/9 = 5/9

Unlike fractions: First find LCD (LCM of denominators). Convert to like fractions. Then add/subtract.
1/3 + 1/4: LCD = 12. 4/12 + 3/12 = 7/12

Mixed fractions: Add/subtract whole parts and fraction parts separately. If fraction subtraction requires borrowing, convert to improper first.

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