Std 6 Mathematics · Chapter 6

6. Fractions

Solutions to Practice Set 6.1 and Exercise 6. Maharashtra State Board (Balbharati), Grade Six Mathematics.

About the chapter

In this chapter, we revise the types of fractions. We learn to compare fractions and arrange them in ascending and descending order. We also add and subtract like fractions, unlike fractions and mixed fractions. Then we solve word problems on fractions.

Key points

Fractions with the same denominator are like fractions. Fractions with different denominators are unlike fractions.
To compare unlike fractions, first make their denominators equal. Then compare the numerators.
To add or subtract like fractions, add or subtract the numerators. The denominator stays the same.
To add or subtract unlike fractions, first take the LCM of the denominators.
Change mixed fractions into improper fractions before adding or subtracting.

Formulas and terms

Proper fraction – numerator is less than the denominator, like 3/5.
Improper fraction – numerator is equal to or more than the denominator, like 7/4.
Mixed fraction – a whole number and a proper fraction together, like 1 3/4.
Unit fraction – a fraction with numerator 1, like 1/8.
a/c + b/c = a + b/c

Practice Set 6.1

1Compare the following fractions.

(i) 8/3 , 5/2

LCM of 3 and 2 = 6
8/3 = 16/6 and 5/2 = 15/6
16 > 15, so 8/3 > 5/2

(ii) 4/9 , 3/7

LCM of 9 and 7 = 63
4/9 = 28/63 and 3/7 = 27/63
28 > 27, so 4/9 > 3/7

(iii) 7/10 , 9/14

LCM of 10 and 14 = 70
7/10 = 49/70 and 9/14 = 45/70
49 > 45, so 7/10 > 9/14

2Write the following fractions in ascending and descending order.

(i) 11/8, 2/4, 7/2

LCM of 8, 4 and 2 = 8
11/8 = 11/8 , 2/4 = 4/8 , 7/2 = 28/8

Ascending order : 2/4 , 11/8 , 7/2

Descending order : 7/2 , 11/8 , 2/4

(ii) 16/9, 5/3, 7/4

LCM of 9, 3 and 4 = 36
16/9 = 64/36 , 5/3 = 60/36 , 7/4 = 63/36

Ascending order : 5/3 , 7/4 , 16/9

Descending order : 16/9 , 7/4 , 5/3

3Solve.

(i) 7/10 + 3/10 = 7 + 3/10 = 10/10 = 1

(ii) 3/4 + 2/6 = 9/12 + 4/12 = 13/12 = 1 1/12

(iii) 1/3 + 7/5 = 5/15 + 21/15 = 26/15 = 1 11/15

(iv) 3/10 + 4/5 = 3/10 + 8/10 = 11/10 = 1 1/10

(v) 5/3 − 2/3 = 5 − 2/3 = 3/3 = 1

(vi) 3/5 − 3/7 = 21/35 − 15/35 = 6/35

4A house is built on 2/5 part of a plot and a garden is made on the remaining part. What part of the plot is the garden?

Whole plot = 1 = 5/5
Part used for the house = 2/5
Part for the garden = 5/5 − 2/5 = 3/5

The garden is made on 3/5 part of the plot.

Exercise 6

1Write the correct number in the blank box.

(i) 5/7 + 2/7 = 7/7 (that is, 1)

(ii) 9/8 − 1/8 = 1 (because 1 = 8/8)

(iii) 6/7 + 6/7 = 12/7 (because 12/7 − 6/7 = 6/7)

(iv) 11/7 − 5/14 = 17/14 (because 22/14 − 17/14 = 5/14)

(v) 16/5 − 0 = 16/5

(vi) 10/5 − 1 = 1 (because 10/5 = 2)

2Solve.

(i) 1/9 + 2/9 = 3/9 = 1/3

(ii) 6/10 + 3/5 = 6/10 + 6/10 = 12/10 = 6/5 = 1 1/5

(iii) 2 2/3 + 3 5/7 = 8/3 + 26/7 = 56/21 + 78/21 = 134/21 = 6 8/21

(iv) 13/4 − 9/4 = 4/4 = 1

(v) 5/4 − 7/8 = 10/8 − 7/8 = 3/8

(vi) 4 1/2 − 2 1/2 = 9/2 − 5/2 = 4/2 = 2

3Out of the 12th pass students of a junior college, 1/5 joined the Indian Army and 2/5 took admission for professional education. What part took admission for higher education?

Students in the army and professional education = 1/5 + 2/5 = 3/5
All students = 1 = 5/5
Remaining students = 5/5 − 3/5 = 2/5

2/5 part of the students took admission for higher education.

4Of the open space in front of a school, 3/4 was for a football field and 1/5 for indoor games. How much space was kept for the school garden?

Space used = 3/4 + 1/5 = 15/20 + 4/20 = 19/20
Whole space = 1 = 20/20
Space for the garden = 20/20 − 19/20 = 1/20

The whole space shown as 20 equal parts — only one part is left for the garden.

1/20 part of the open space was kept for the school garden.

5Mother gave one guava each to Ramesh, Seema and their three friends. Each divided the guava into four equal parts and gave one part to mother. What part of a guava did mother get?

Number of children = 2 + 3 = 5
Each child gave 1/4 part to mother.
Mother got = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4 = 1 1/4

Mother got 1 1/4 guavas.

66/7 is less than 9/11 because 6 is less than 9. Is this correct?

No, this is not correct. We can compare numerators only when the denominators are the same.

LCM of 7 and 11 = 77
6/7 = 66/77 and 9/11 = 63/77
66 > 63, so 6/7 > 9/11

So, 6/7 is greater than 9/11.

7Write any two fractions whose sum is 1.

1/4 + 3/4 = 4/4 = 1
3/8 + 5/8 = 8/8 = 1

So, 1/4 and 3/4 or 3/8 and 5/8 are two fractions whose sum is 1.

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