Class 5 Mathematics · Chapter 2

2. Fractions

Solutions to all Let Us Do, Try This and in-chapter questions. CBSE / NCERT Class 5 Maths Mela.

Introduction

1Tamanna says that 13 of one of her chocolates is bigger than 12 of the other chocolate. Is that correct? Explain why.

Yes, it can be correct.

Her two chocolates are of different sizes.

13 of a big chocolate can be bigger than 12 of a small chocolate.

2When can we say that 12 of something is greater than 13 of something?

Only when both fractions are taken from the same whole (or equal wholes), 12 > 13.

Playing with a Grid

1Shade 18 of Grid A in red, 16 of Grid B in blue and 112 of Grid C in yellow. Do you see 13 in any of the grids?

Each grid has 8 columns and 6 rows. So, each grid has 8 × 6 = 48 squares.

18 of 48 = 6 squares. Shade 6 squares of Grid A in red.

16 of 48 = 8 squares. Shade 8 squares (one full row) of Grid B in blue.

112 of 48 = 4 squares. Shade 4 squares of Grid C in yellow.

13 of 48 = 16 squares. None of the shaded parts is 13. Mark 2 full rows (16 squares) in any grid to show 13.

2Is 13 equal to 26? Are there two different ways to write the fraction represented by the shaded part?

Yes. The shaded part can be written as 13 or 26.

So, 13 = 26. These are equivalent fractions.

Fun with Fraction Kit

1How many 15 pieces will you need to make a whole?

5 pieces of 15 make a whole.

2What is the relation between 12 and 14? What else is equivalent to 12?

14 is half of 12. Two 14 pieces make 12.

12 = 24 = 36 = 48 = 612

Let Us Do

1Write the equivalent fractions for the following.

(a) 13 = 26 = 39 = 412

(b) 14 = 28 = 312 = 416

(d) 16 = 212 = 318 = 424

How to generate equivalent fractions: Multiply the numerator and the denominator by the same number.

2Find the following using your kit.

A. 2 pieces of 16 make 13.

B. (a) 2 pieces of 18 make 14. (b) 4 pieces of 18 make 12.

C. (a) 6 pieces of 112 make 12. (b) 4 make 13. (c) 3 make 14. (d) 2 make 16.

3Do as instructed using your fraction kit.

Using only 16 and 112: 4 pieces of 16 + 4 pieces of 112 = 1 whole.

Using 112, 14 and 12: 1 piece of 12 + 1 piece of 14 + 3 pieces of 112 = 1 whole.

Using five pieces of the same size: 5 pieces of 15 = 1 whole.

Using any seven pieces: 1 piece of 12 + 6 pieces of 112 = 1 whole.

Other combinations are also possible.

Making Equivalent Fractions

1Divide the wholes into more equal parts and find fractions equivalent to 13. Do you see any pattern?

Dividing each part into 2, 3 and 4 equal parts gives 26, 39 and 412.

13 = 26 = 39 = 412 = 515 = 618 = 721 = 824 = 1236

Pattern: the denominator is always 3 times the numerator.

2How do you know when a fraction is equivalent to another?

When we multiply (or divide) the numerator and the denominator of a fraction by the same number, we get an equivalent fraction.

3Find the different fractions that are equivalent to 25.

25 = 410 = 615 = 820 = 2050 = 40100

Let Us Do

1Fill in the blanks with equivalent fractions. There may be more than one answer.

(a) 17 = 214
(b) 23 = 46
(c) 34 = 68
(d) 35 = 610

2Put a tick (✓) against the fractions that are equivalent.

(a) 23 and 34 — ✗ Not equivalent.

(b) 35 and 610 — ✓ Equivalent

(d) 69 and 13 — ✗ Not equivalent. (69 = 23)

3Fill in the boxes such that the fractions become equivalent.

(a) 25 = 410
(b) 34 = 1216
(c) 47 = 814
(d) 59 = 2545

Comparing Fractions — Same Denominator

1Compare the fractions given below using < and > signs.

(a) 14 < 34
(b) 35 < 45
(c) 57 > 27

(d) 78 > 38
(e) 510 < 610
(f) 26 > 16

When the denominators are the same, the fraction with the bigger numerator is bigger.

Comparing Fractions — Same Numerator

1Sevi ate 46 paratha and Shami ate 45 paratha. Who ate more?

A 16 piece is smaller than a 15 piece.

So, 46 < 45. Shami ate more.

2Compare the following fractions using < and > signs.

(a) 38 < 37
(b) 49 > 410
(c) 27 < 25

(d) 57 < 56
(e) 69 > 610
(f) 79 > 711

When the numerators are the same, the fraction with the smaller denominator is bigger.

Fractions Greater Than 1

1Dadiji had 7 pieces of 12 paratha. How many parathas did she eat?

7 pieces of 12 = 72 = 3 + 12 = 312 parathas

2Raman ate 6 pieces, Dadaji ate 7 pieces and Baba ate 5 pieces of 12 paratha. How many parathas did each of them eat? How many parathas were made on this day?

Raman: 62 = 3 parathas

Dadaji: 72 = 312 parathas

Baba: 52 = 212 parathas

On the number line, divide each 1 into 2 equal parts and jump 6, 7 and 5 halves.

Parathas made that day (Maa 5, Radhika 6, Dadiji 7, Raman 6, Dadaji 7, Baba 5 halves):

5 + 6 + 7 + 6 + 7 + 5 = 36 halves = 362 = 18 parathas

3Raman ate 7, Radhika 6, Maa 8, Dadiji 10 and Baba 12 pieces of 14 paratha. How many parathas were eaten by each? How many parathas were made on this day?

Raman: 74 = 134 parathas

Radhika: 64 = 124 or 112 parathas

Maa: 84 = 2 parathas

Dadiji: 104 = 224 or 212 parathas

Baba: 124 = 3 parathas

Including Dadaji’s 9 pieces: 9 + 7 + 6 + 8 + 10 + 12 = 52 fourths = 524 = 13 parathas

4Raman’s family of 6 ordered 2 pizzas, each cut into 3 equal slices. Dadiji and Dadaji gave their slices to Raman. Maa and Baba gave theirs to Radhika. How much pizza does each of them have? Then Raman gave 1 slice to Radhika. How much does Radhika have now?

Raman: 13 + 13 + 13 = 33 = 1 whole pizza

Radhika: 13 + 13 + 13 = 33 = 1 whole pizza

Dadiji, Dadaji, Maa and Baba have no pizza now.

After Raman gives 1 slice, Raman has 23 pizza.

Radhika has 43 = 1 + 13 = 113 pizza.

Let Us Do

1Use parathas and number lines to show the following fractions.

(a) 23: divide 0 to 1 into 3 equal parts and take 2 parts. 53 = 123: take 5 such parts. It lies between 1 and 2.

(b) 34: divide 0 to 1 into 4 equal parts and take 3 parts. 54 = 114: it lies just after 1.

2Circle the fractions that are greater than one (whole). How do you know?

Circle: 94, 94, 54, 73, 1311, 125, 128

In these fractions, the numerator is greater than the denominator. So, they are more than one whole.

Comparing Fractions with Reference to 1

1Compare the following fractions using 1 as a reference.

(a) 87 > 915 — 87 is more than 1. 915 is less than 1.

(b) 1320 < 1715 — 1320 is less than 1. 1715 is more than 1.

(d) 66 < 1912 — 66 is exactly 1. 1912 is more than 1.

(e) 129 > 45 — 129 is more than 1. 45 is less than 1.

(f) 155 < 164 — Both are more than 1. 155 = 3 and 164 = 4.

Comparing Fractions with Reference to 12

1Circle the fractions below that are equal to 12.

Circle: 24, 714, 510, 816, 612, 1020

In each of these, the numerator is exactly half of the denominator.

2Circle the fractions that are less than half. How do you know?

Circle: 39, 315, 13, 1531, 618

In these fractions, the numerator is less than half of the denominator.

24 and 48 are equal to half, so they are not circled.

3Who ate more paratha — the one who ate 58 or the one who ate 36?

36 is exactly half. 58 is more than half.

So, 58 > 36. The one who ate 58 paratha ate more.

4Compare the following fractions. Where possible, compare the fractions with 12.

29 < 47
1114 > 720
57 > 39
67 > 410

917 > 315
712 > 311
13 < 59
39 < 47

In each pair, one fraction is more than 12 and the other is less than 12.

Try This

1If the length of an ant is 14 cm, what is the total length of 16 such ants walking in a line?

16 × 14 cm = 164 cm = 4 cm

On the number line, 4 ants make 1 cm. So, 16 ants make 4 cm.

Fun with Relations

1If the only brother of your father’s sister had a child, what would be the child’s relationship with you?

The only brother of your father’s sister is your father.

So, the child is you or your own brother or sister.

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