Class 6 Mathematics · Chapter 7

7. Fractions

Answers to all questions on fractional units, mixed fractions, equivalent fractions, comparing, adding and subtracting fractions. CBSE / NCERT Class 6 Ganita Prakash.

7.1 Fractional Units and Equal Shares — Figure it Out

1Three guavas together weigh 1 kg. Each guava will roughly weigh ____ kg.

Each guava weighs about 13 kg.

21 kg of rice is packed in four packets of equal weight. Each packet weighs ____ kg.

Each packet weighs 14 kg.

3Four friends shared 3 glasses of sugarcane juice equally. Each one drank ____ glass.

3 ÷ 4 = 34 glass each.

4The big fish weighs 12 kg and the small one weighs 14 kg. Together they weigh ____ kg.

12 + 14 = 24 + 14 = 34 kg

5Arrange from smallest to biggest: one and a half, three quarters, one and a quarter, half, quarter, two and a half.

Quarter (14) < half (12) < three quarters (34) < one and a quarter (114) < one and a half (112) < two and a half (212)

7.2 Fractional Units as Parts of a Whole

★By dividing the whole chikki into 6 equal parts in different ways, we get 16 chikki pieces of different shapes. Are they of the same size?

Yes. Each piece is one of 6 equal parts of the same chikki, so each is 16 of it, even though the shapes are different.

★Figure it Out: How much of a whole chikki is each piece?

(a) 112 (b) 14 (c) 18 (d) 16

(e) 18 (f) 16 (g) 124 (h) 124

7.3 Measuring Using Fractional Units

★Do it once more! Fill in the blank boxes (strip folded into 8 equal parts).

1 × 18 = 18

2 × 18 = 28 3 × 18 = 38

4 × 18 = 48 5 × 18 = 58

6 × 18 = 68 7 × 18 = 78

8 × 18 = 88 = 1

7.3 — Figure it Out

1Continue the table of 12 for 2 more steps.

12 + 12 + 12 + 12 + 12 + 12 = 6 times half = 3

12 + 12 + 12 + 12 + 12 + 12 + 12 = 7 times half = 312

2Can you create a similar table for 14?

14 = 1 times quarter

14 + 14 = 2 times quarter = 24

14 + 14 + 14 = 3 times quarter = 34

14 + 14 + 14 + 14 = 4 times quarter = 1

3Make 13 using a paper strip. Can you use this to also make 16?

Fold the strip into 3 equal parts (like folding a letter). Each part is 13.

Now fold the strip in half again. Each part becomes 16. Yes, 16 can be made from 13.

4Draw a picture and write an addition statement for (a) 5 times 14 of a roti (b) 9 times 14 of a roti.

(a) 14 + 14 + 14 + 14 + 14 = 54 = 1 roti and 14 roti

(b) 14 added 9 times = 94 = 2 rotis and 14 roti

Draw rotis cut into 4 equal parts and shade the required number of parts.

5Match each fractional unit with the correct picture.

13 → third circle (3 equal parts)

15 → fourth circle (5 equal parts)

18 → first circle (8 equal parts)

16 → second circle (6 equal parts)

7.4 Marking Fraction Lengths on the Number Line

★Find the lengths of the blue lines.

1. Unit divided into 3 parts: the blue line is 23 unit long.

2. Unit divided into 5 parts: the blue lines are 25 and 45 unit long.

3. Unit divided into 8 parts: the marks are 18, 28, 38, 48, 58, 68, 78.

7.4 — Figure it Out

1On a number line, draw lines of lengths 110, 310 and 45.

Divide 0 to 1 into 10 equal parts. Draw lines up to the 1st mark (110) and the 3rd mark (310).

For 45, divide 0 to 1 into 5 equal parts and draw a line up to the 4th mark. (It is the same as 810.)

2Write five more fractions and mark them on the number line.

For example: 14, 12, 23, 56, 32. Divide each unit into the required number of equal parts and mark them.

3How many fractions lie between 0 and 1?

Countless (infinitely many). We can always divide a unit into more and more equal parts, for example 12, 13, 1100, 11000, …

4What is the length of the black line?

The black line is 32 units long (3 half units).

5Write the fractions that give the lengths of the black lines.

65, 75, 85, 95

7.5 Mixed Fractions — Figure it Out

1How many whole units are there in 72?

72 = 3 + 12. So there are 3 whole units.

2How many whole units are there in 43 and in 73?

43 = 1 + 13 → 1 whole unit

73 = 2 + 13 → 2 whole units

★Figure out the number of whole units in (a) 83 (b) 115 (c) 94.

(a) 83 = 2 + 23 → 2 (b) 115 = 2 + 15 → 2 (c) 94 = 2 + 14 → 2

★Can all fractions greater than 1 be written as mixed numbers?

Yes, every fraction greater than 1 can be written as a whole number and a fraction less than 1.

But if the fraction is exactly a whole number, like 63 = 2, there is no fractional part left.

★Write as mixed fractions: (a) 92 (b) 95 (c) 2119 (d) 479 (e) 1211 (f) 196

(a) 412 (b) 145 (c) 1219

(d) 529 (e) 1111 (f) 316

★Write the mixed numbers as fractions: (a) 314 (b) 723 (c) 949 (d) 316 (e) 2311 (f) 3910

(a) 314 = 3 × 4 + 14 = 134

(b) 723 = 7 × 3 + 23 = 233

(d) 316 = 3 × 6 + 16 = 196

(e) 2311 = 2 × 11 + 311 = 2511

(f) 3910 = 3 × 10 + 910 = 3910

7.6 Equivalent Fractions

★Answer using the fraction wall.

1. Yes, 12 and 36 are equal lengths.

2. Yes, 23 and 46 are equivalent. They have the same length on the fraction wall.

3. 3 pieces of 16 make 12.

4. 2 pieces of 16 make 13.

1Are 36, 48, 510 equivalent fractions? Why?

Yes. Each of them is equal to 12. They have the same length on the fraction wall.

2Write two equivalent fractions for 26.

13 and 412

346 = ___ = ___ = ___ (Write as many as you can)

46 = 23 = 69 = 812 = 1015 = 1218 = …

Equivalent Fractions using Equal Shares — Figure it Out

1Three rotis are shared equally by four children. How much does each child get? Write the facts.

Each child gets 34 roti.

Division fact: 3 ÷ 4 = 34

Addition fact: 34 + 34 + 34 + 34 = 3

Multiplication fact: 4 × 34 = 3

22 rotis are shared equally by 4 children. Write the facts.

Each child gets 24 = 12 roti.

Division fact: 2 ÷ 4 = 24 = 12

Addition fact: 12 + 12 + 12 + 12 = 2

Multiplication fact: 4 × 12 = 2

32 cakes were divided equally among 5 children. How much cake would Anil get? With 10 children, how many cakes are needed for the same share?

Anil gets 25 cake.

With 10 children, 4 cakes are needed. So 25 = 410.

★Find some more fractions equivalent to 12.

48, 510, 612, 1020

★2 rotis among 3 children, 4 rotis among 6, 6 rotis among 9. Are the shares the same? What do you notice?

Each child gets 23 roti in every case, so the shares are the same: 23 = 46 = 69.

In 46 and 69, the numerator and denominator of 23 are multiplied by the same number (2 and 3).

★Find the missing numbers.

(a) 5 glasses among 4 friends = 10 glasses among 8 friends. So 54 = 108.

(b) 4 kg in 3 bags = 12 kg in 9 bags. So 43 = 129.

★If the number of children is the same but more units are shared, what happens to each share? Explain 15 < 25, 37 < 47 and 12 < 58.

Each child gets a bigger share, because more units are shared among the same number of children.

12 = 48, and 5 units among 8 is more than 4 units among 8. So 12 < 58.

★In which group will each child get a larger share?

1. Group 1: 34 = 3040; Group 2: 710 = 2840. Group 1 gets more.

2. Group 1: 47; Group 2: 57. Group 2 gets more.

The second pair was easier to compare, because the number of children (denominator) was the same.

★Find equivalent fractions with the same fractional unit for the given pairs.

Pair	Same fractional unit
72 and 35	3510 and 610
83 and 56	166 and 56
34 and 35	1520 and 1220
67 and 85	3035 and 5635
94 and 52	94 and 104
110 and 29	990 and 2090
83 and 114	3212 and 3312
136 and 19	3918 and 218

Lowest Terms — Figure it Out

★Express in lowest terms: (a) 1751 (b) 64144 (c) 126147 (d) 525112

(a) Divide by 17: 1751 = 13

(b) Divide by 16: 64144 = 49

(d) Divide by 7: 525112 = 7516

7.7 Comparing Fractions — Figure it Out

1Compare and justify: (a) 83, 52 (b) 49, 37 (c) 710, 914 (d) 125, 85 (e) 94, 52

(a) 166 and 156. So 83 > 52

(b) 2863 and 2763. So 49 > 37

(d) Same denominator, 12 > 8. So 125 > 85

(e) 52 = 104. So 94 < 52

2Write in ascending order: (a) 710, 1115, 25 (b) 1924, 56, 712

(a) 2130, 2230, 1230 → 25 < 710 < 1115

(b) 1924, 2024, 1424 → 712 < 1924 < 56

3Write in descending order: (a) 2516, 78, 134, 1732 (b) 34, 125, 712, 54

(a) 5032, 2832, 10432, 1732 → 134 > 2516 > 78 > 1732

(b) 4560, 14460, 3560, 7560 → 125 > 54 > 34 > 712

7.8 Addition and Subtraction of Fractions

★Meena ate 12 and her brother ate 14 of the chikki. How much of the chikki is remaining?

Eaten = 34. Remaining = 1 − 34 = 14 of the chikki.

★Try adding 47 + 67 using a number line.

Start at 47 and move 6 more steps of 17. We reach 107 = 137. Yes, the answer is the same.

Addition — Figure it Out

1Add using Brahmagupta’s method.

(a) 27 + 57 + 67 = 137 = 167

(b) 912 + 412 = 1312 = 1112

(d) 1421 + 621 = 2021

(e) 4560 + 2060 + 1260 = 7760 = 11760

(f) 1015 + 1215 = 2215 = 1715

(g) 1215 + 1015 = 2215 = 1715

(h) 2440 + 2540 = 4940 = 1940

(i) 184 + 54 = 234 = 534

(j) 5621 + 621 = 6221 = 22021

(k) 4560 + 2060 + 1260 = 7760 = 11760

(l) 70105 + 84105 + 45105 = 199105 = 194105

(m) 5412 + 1512 + 1412 = 8312 = 61112

2Rahim mixes 23 litre of yellow paint with 34 litre of blue paint. What is the volume of green paint?

23 + 34 = 812 + 912 = 1712 = 1512 litres

3Geeta bought 25 m of lace and Shamim bought 34 m. The border is 1 m long. Find the total lace. Is it sufficient?

25 + 34 = 820 + 1520 = 2320 = 1320 m

Yes, it is sufficient, because 1320 m is more than 1 m.

Subtraction — Figure it Out

★Subtract: 1. 58 − 38 2. 79 − 59 3. 1027 − 127

1. 28 = 14

2. 29

3. 927 = 13

1Subtract using Brahmagupta’s method: (a) 815 − 315 (b) 25 − 415 (c) 56 − 49 (d) 23 − 12

(a) 515 = 13

(b) 615 − 415 = 215

(d) 46 − 36 = 16

2Subtract as indicated: (a) 134 from 103 (b) 185 from 233 (c) 297 from 457

(a) 103 − 134 = 4012 − 3912 = 112

(b) 233 − 185 = 11515 − 5415 = 6115 = 4115

3(a) Jaya’s school is 710 km away. She takes an auto for 12 km and walks the rest. How much does she walk? (b) Jeevika takes 103 minutes and Namit takes 134 minutes for a round of the park. Who takes less time and by how much?

(a) 710 − 12 = 710 − 510 = 210 = 15 km

(b) 103 = 4012 and 134 = 3912. Namit takes less time, by 112 minute.

Puzzle!

1Find three different fractional units that add up to 1.

12 + 13 + 16 = 36 + 26 + 16 = 1

2Find four different fractional units that add up to 1. (There are six solutions.)

12 + 13 + 17 + 142

12 + 13 + 18 + 124

12 + 13 + 19 + 118

12 + 13 + 110 + 115

12 + 14 + 15 + 120

12 + 14 + 16 + 112

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