CLASS 5 · MATHS MELA · CHAPTER 2

Fractions

Use equal pieces to understand fractions, compare them and find shares larger than one whole. Short working, original fraction strips and number lines help you see each answer.

87 worked answers

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87 worked answers · short steps first, explanations when you need them

Chocolate sizes and grids

Textbook pages 17

Question Chocolate sizes

Can one-third of a large chocolate be greater than one-half of a small chocolate?

Steps only

Yes, the whole chocolates can have different sizes.

1/3 of 60 g = 20 g

1/2 of 30 g = 15 g

20 g > 15 g

Answer

Yes. Compare fractions directly only when the whole is the same size.

Question Grid A

The grid has 48 equal cells. How many cells show 1/8 of the whole?

Steps only

48 ÷ 8 = 6

6/48 = 1/8 · each grid is one whole

Answer

Shade 6 cells.

Question Grid B

The grid has 48 equal cells. How many cells show 1/6 of the whole?

Steps only

48 ÷ 6 = 8

8/48 = 1/6 · each grid is one whole

Answer

Shade 8 cells.

Question Grid C

The grid has 48 equal cells. How many cells show 1/12 of the whole?

Steps only

48 ÷ 12 = 4

4/48 = 1/12 · each grid is one whole

Answer

Shade 4 cells.

Question One-third grid

How can you mark one-third in each 48-cell grid?

Steps only

48 ÷ 3 = 16

16/48 = 1/3 · each grid is one whole

Answer

Mark 16 cells in each grid.

Fraction-kit ideas

Textbook pages 18

Question Fifths in a whole

How many one-fifth pieces make one whole?

Steps only

5 × 1/5 = 5/5 = 1

5/5 · each bar is one whole

Answer

5 pieces.

Question Halves and quarters

How many quarter pieces cover the same amount as one half?

Steps only

1/2 = 2/4

1/2 · each bar is one whole

2/4 · each bar is one whole

Answer

2 quarter pieces.

Question Equivalent halves

Continue 1/2 = 2/4 with three more equivalent fractions.

Steps only

1/2 = 2/4 = 3/6 = 4/8 = 5/10

Answer

Examples: 3/6, 4/8 and 5/10.

Let Us Do: equivalent pieces

Textbook pages 19

Question 1(a)

Write three fractions equivalent to 1/3.

Steps only

1/3 = 2/6 = 3/9 = 4/12

Answer

2/6, 3/9, 4/12

Question 1(b)

Write three fractions equivalent to 1/4.

Steps only

1/4 = 2/8 = 3/12 = 4/16

Answer

2/8, 3/12, 4/16

Question 1(c)

Write three fractions equivalent to 1/5.

Steps only

1/5 = 2/10 = 3/15 = 4/20

Answer

2/10, 3/15, 4/20

Question 1(d)

Write three fractions equivalent to 1/6.

Steps only

1/6 = 2/12 = 3/18 = 4/24

Answer

2/12, 3/18, 4/24

Question 2A

How many 1/6 pieces make 1/3?

Steps only

1/3 = 2/6

1/3 · each bar is one whole

2/6 · each bar is one whole

Answer

2 pieces.

Question 2B(a)

How many 1/8 pieces make 1/4?

Steps only

1/4 = 2/8

1/4 · each bar is one whole

2/8 · each bar is one whole

Answer

2 pieces.

Question 2B(b)

How many 1/8 pieces make 1/2?

Steps only

1/2 = 4/8

1/2 · each bar is one whole

4/8 · each bar is one whole

Answer

4 pieces.

Question 2C(a)

How many 1/12 pieces make 1/2?

Steps only

1/2 = 6/12

1/2 · each bar is one whole

6/12 · each bar is one whole

Answer

6 pieces.

Question 2C(b)

How many 1/12 pieces make 1/3?

Steps only

1/3 = 4/12

1/3 · each bar is one whole

4/12 · each bar is one whole

Answer

4 pieces.

Question 2C(c)

How many 1/12 pieces make 1/4?

Steps only

1/4 = 3/12

1/4 · each bar is one whole

3/12 · each bar is one whole

Answer

3 pieces.

Question 2C(d)

How many 1/12 pieces make 1/6?

Steps only

1/6 = 2/12

1/6 · each bar is one whole

2/12 · each bar is one whole

Answer

2 pieces.

Let Us Do: making a whole

Textbook pages 20

Question 3 · sixths and twelfths

Make a whole using both sixths and twelfths.

Steps only

4/6 + 4/12 = 8/12 + 4/12 = 1

Answer

4 sixths and 4 twelfths.

Question 3 · three sizes

Make a whole using twelfths, quarters and halves.

Steps only

3/12 + 1/4 + 1/2 = 3/12 + 3/12 + 6/12 = 1

Answer

3 twelfths, 1 quarter and 1 half.

Question 3 · five equal pieces

Make a whole with five pieces of the same size.

Steps only

5 × 1/5 = 1

Answer

Five one-fifth pieces.

Question 3 · seven pieces

Give one way to make a whole with seven fraction-kit pieces.

Steps only

1/2 + 6/12 = 6/12 + 6/12 = 1

Answer

One half and six twelfths.

Equivalent-fraction patterns

Textbook pages 21

Question Thirds pattern

Complete the equivalent-thirds pattern, including the fractions with denominators 24 and 36.

Steps only

1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 = 7/21 = 8/24 = 12/36

Answer

5/15, 6/18, 7/21, 8/24 and 12/36.

Question Two-fifths pattern

Complete 2/5 = 4/10 with the next two fractions and fractions with denominators 50 and 100.

Steps only

2/5 = 4/10 = 6/15 = 8/20 = 20/50 = 40/100

Answer

6/15, 8/20, 20/50 and 40/100.

Let Us Do: checking equivalence

Textbook pages 22

Question 1(a)

Give one fraction equal to 1/7.

Steps only

1/7 = (1 × 2)/(7 × 2) = 2/14

Answer

2/14

Question 1(b)

Give one fraction equal to 2/3.

Steps only

2/3 = (2 × 2)/(3 × 2) = 4/6

Answer

4/6

Question 1(c)

Give one fraction equal to 3/4.

Steps only

3/4 = (3 × 2)/(4 × 2) = 6/8

Answer

6/8

Question 1(d)

Give one fraction equal to 3/5.

Steps only

3/5 = (3 × 2)/(5 × 2) = 6/10

Answer

6/10

Question 2(a)

Are 2/3 and 3/4 equivalent?

Steps only

2/3 = 2/3

3/4 = 3/4

Answer

No, do not tick the pair.

Question 2(b)

Are 3/5 and 6/10 equivalent?

Steps only

3/5 = 3/5

6/10 = 3/5

Answer

Yes, tick the pair.

Question 2(c)

Are 4/12 and 2/6 equivalent?

Steps only

4/12 = 1/3

2/6 = 1/3

Answer

Yes, tick the pair.

Question 2(d)

Are 6/9 and 1/3 equivalent?

Steps only

6/9 = 2/3

1/3 = 1/3

Answer

No, do not tick the pair.

Question 3(a)

Fill the missing numerator in 2/5 = ?/10.

Steps only

2/5 = (2 × 2)/(5 × 2) = 4/10

Answer

Question 3(b)

Fill the missing numerator in 3/4 = ?/16.

Steps only

3/4 = (3 × 4)/(4 × 4) = 12/16

Answer

Question 3(c)

Fill the missing denominator in 4/7 = 8/?.

Steps only

4/7 = (4 × 2)/(7 × 2) = 8/14

Answer

Question 3(d)

Fill the missing denominator in 5/9 = 25/?.

Steps only

5/9 = (5 × 5)/(9 × 5) = 25/45

Answer

Let Us Do: same denominator

Textbook pages 23

Question 1(a)

Compare 1/4 and 3/4 using < or >.

Steps only

Equal-sized 4ths: compare 1 and 3.

1/4 < 3/4

Answer

1/4 < 3/4

Question 1(b)

Compare 3/5 and 4/5 using < or >.

Steps only

Equal-sized 5ths: compare 3 and 4.

3/5 < 4/5

Answer

3/5 < 4/5

Question 1(c)

Compare 5/7 and 2/7 using < or >.

Steps only

Equal-sized 7ths: compare 5 and 2.

5/7 > 2/7

Answer

5/7 > 2/7

Question 1(d)

Compare 7/8 and 3/8 using < or >.

Steps only

Equal-sized 8ths: compare 7 and 3.

7/8 > 3/8

Answer

7/8 > 3/8

Question 1(e)

Compare 5/10 and 6/10 using < or >.

Steps only

Equal-sized 10ths: compare 5 and 6.

5/10 < 6/10

Answer

5/10 < 6/10

Question 1(f)

Compare 2/6 and 1/6 using < or >.

Steps only

Equal-sized 6ths: compare 2 and 1.

2/6 > 1/6

Answer

2/6 > 1/6

Let Us Do: same numerator

Textbook pages 23

Question 1(a)

Compare 3/8 and 3/7 using < or >.

Steps only

The smaller denominator gives larger pieces.

3/8 < 3/7

Answer

3/8 < 3/7

Question 1(b)

Compare 4/9 and 4/10 using < or >.

Steps only

The smaller denominator gives larger pieces.

4/9 > 4/10

Answer

4/9 > 4/10

Question 1(c)

Compare 2/7 and 2/5 using < or >.

Steps only

The smaller denominator gives larger pieces.

2/7 < 2/5

Answer

2/7 < 2/5

Question 1(d)

Compare 5/7 and 5/6 using < or >.

Steps only

The smaller denominator gives larger pieces.

5/7 < 5/6

Answer

5/7 < 5/6

Question 1(e)

Compare 6/9 and 6/10 using < or >.

Steps only

The smaller denominator gives larger pieces.

6/9 > 6/10

Answer

6/9 > 6/10

Question 1(f)

Compare 7/9 and 7/11 using < or >.

Steps only

The smaller denominator gives larger pieces.

7/9 > 7/11

Answer

7/9 > 7/11

Parathas cut into halves

Textbook pages 24–25

Question Maa

How many whole parathas are 5 half-paratha pieces?

Steps only

5 × 1/2 = 5/2

5/2 = 2 + 1/2

Each whole is divided into 2 equal parts.

Answer

2 1/2 parathas.

Question Radhika

How many whole parathas are 6 half-paratha pieces?

Steps only

6 × 1/2 = 6/2

6/2 = 3

Each whole is divided into 2 equal parts.

Answer

3 parathas.

Question Dadiji

How many whole parathas are 7 half-paratha pieces?

Steps only

7 × 1/2 = 7/2

7/2 = 3 + 1/2

Each whole is divided into 2 equal parts.

Answer

3 1/2 parathas.

Question Raman

How many whole parathas are 6 half-paratha pieces?

Steps only

6 × 1/2 = 6/2

6/2 = 3

Each whole is divided into 2 equal parts.

Answer

3 parathas.

Question Dadaji

How many whole parathas are 7 half-paratha pieces?

Steps only

7 × 1/2 = 7/2

7/2 = 3 + 1/2

Each whole is divided into 2 equal parts.

Answer

3 1/2 parathas.

Question Baba

How many whole parathas are 5 half-paratha pieces?

Steps only

5 × 1/2 = 5/2

5/2 = 2 + 1/2

Each whole is divided into 2 equal parts.

Answer

2 1/2 parathas.

Question Total halves

Find the total parathas eaten by the six family members in the half-piece story.

Steps only

(5 + 6 + 7 + 6 + 7 + 5)/2

= 36/2 = 18

Answer

18 parathas.

Parathas and pizzas

Textbook pages 26–28

Question Dadaji

How many parathas are 9 quarter-paratha pieces?

Steps only

9 × 1/4 = 9/4

9/4 = 2 + 1/4

9/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

2 1/4 parathas.

Question Raman

How many parathas are 7 quarter-paratha pieces?

Steps only

7 × 1/4 = 7/4

7/4 = 1 + 3/4

7/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

1 3/4 parathas.

Question Radhika

How many parathas are 6 quarter-paratha pieces?

Steps only

6 × 1/4 = 6/4

6/4 = 1 + 1/2

6/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

1 1/2 parathas.

Question Maa

How many parathas are 8 quarter-paratha pieces?

Steps only

8 × 1/4 = 8/4

8/4 = 2

8/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

2 parathas.

Question Dadiji

How many parathas are 10 quarter-paratha pieces?

Steps only

10 × 1/4 = 10/4

10/4 = 2 + 1/2

10/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

2 1/2 parathas.

Question Baba

How many parathas are 12 quarter-paratha pieces?

Steps only

12 × 1/4 = 12/4

12/4 = 3

12/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

3 parathas.

Question Total quarters

Find the total parathas eaten in the quarter-piece story.

Steps only

(9 + 7 + 6 + 8 + 10 + 12)/4

= 52/4 = 13

Answer

13 parathas.

Question Pizza shares

After the older family members give away their pizza thirds, how much do Raman and Radhika each have?

Steps only

1/3 + 1/3 + 1/3 = 3/3 = 1

3/3 · each bar is one whole

Answer

Each has 1 whole pizza.

Question One more pizza slice

Raman gives one of his three pizza thirds to Radhika. How much pizza does Radhika now have?

Steps only

3/3 + 1/3 = 4/3

= 1 + 1/3

4/3 · each bar is one whole

Each whole is divided into 3 equal parts.

Answer

1 1/3 pizzas.

Let Us Do: fractions above one

Textbook pages 28

Question 1(a)

Show 2/3 and 5/3 with equal parts and on a number line.

Steps only

Split every whole unit into 3 equal parts.

Count 2 parts and 5 parts from 0.

2/3 · each bar is one whole

5/3 · each bar is one whole

Each whole is divided into 3 equal parts.

Answer

The marked positions are 2/3 and 5/3.

Question 1(b)

Show 3/4 and 5/4 with equal parts and on a number line.

Steps only

Split every whole unit into 4 equal parts.

Count 3 parts and 5 parts from 0.

3/4 · each bar is one whole

5/4 · each bar is one whole

Each whole is divided into 4 equal parts.

Answer

The marked positions are 3/4 and 5/4.

Question 1(c)

Show 4/8 and 9/8 with equal parts and on a number line.

Steps only

Split every whole unit into 8 equal parts.

Count 4 parts and 9 parts from 0.

4/8 · each bar is one whole

9/8 · each bar is one whole

Each whole is divided into 8 equal parts.

Answer

The marked positions are 4/8 and 9/8.

Question 2

Which fractions in the page 28 box are greater than one whole?

Steps only

Choose fractions whose top number is greater than the bottom number.

9/4, 5/4, 7/3, 13/11, 12/5, 12/8

Answer

9/4 (appears twice), 5/4, 7/3, 13/11, 12/5 and 12/8.

Let Us Do: compare with a whole

Textbook pages 29

Question 1(a)

Compare 8/7 and 9/15 using one whole.

Steps only

8/7 > 1

9/15 < 1

8/7 > 9/15

Answer

8/7 > 9/15

Question 1(b)

Compare 13/20 and 17/15 using one whole.

Steps only

13/20 < 1

17/15 > 1

13/20 < 17/15

Answer

13/20 < 17/15

Question 1(c)

Compare 7/6 and 8/8 using one whole.

Steps only

7/6 > 1

8/8 = 1

7/6 > 8/8

Answer

7/6 > 8/8

Question 1(d)

Compare 6/6 and 19/12 using one whole.

Steps only

6/6 = 1

19/12 > 1

6/6 < 19/12

Answer

6/6 < 19/12

Question 1(e)

Compare 12/9 and 4/5 using one whole.

Steps only

12/9 > 1

4/5 < 1

12/9 > 4/5

Answer

12/9 > 4/5

Question 1(f)

Compare 15/5 and 16/4 using one whole.

Steps only

15/5 > 1

16/4 > 1

15/5 < 16/4

Answer

15/5 < 16/4

Let Us Do: equal to or below half

Textbook pages 30

Question 1

Choose the fractions equal to one-half from the page 30 box.

Steps only

2/4 = 7/14 = 5/10 = 8/16 = 6/12 = 10/20 = 1/2

Answer

2/4, 7/14, 5/10, 8/16, 6/12 and 10/20.

Question 2

Choose the fractions less than one-half from the page 30 box.

Steps only

2 × 3 < 9; 2 × 3 < 15; 2 × 1 < 3

2 × 15 < 31; 2 × 6 < 18

Answer

3/9, 3/15, 1/3, 15/31 and 6/18.

More comparisons and Try This

Textbook pages 31

Question 3 · pair 1

Compare 2/9 and 4/7 using one-half.

Steps only

2/9 < 1/2

4/7 > 1/2

2/9 < 4/7

Answer

2/9 < 4/7

Question 3 · pair 2

Compare 11/14 and 7/20 using one-half.

Steps only

11/14 > 1/2

7/20 < 1/2

11/14 > 7/20

Answer

11/14 > 7/20

Question 3 · pair 3

Compare 5/7 and 3/9 using one-half.

Steps only

5/7 > 1/2

3/9 < 1/2

5/7 > 3/9

Answer

5/7 > 3/9

Question 3 · pair 4

Compare 6/7 and 4/10 using one-half.

Steps only

6/7 > 1/2

4/10 < 1/2

6/7 > 4/10

Answer

6/7 > 4/10

Question 3 · pair 5

Compare 9/17 and 3/15 using one-half.

Steps only

9/17 > 1/2

3/15 < 1/2

9/17 > 3/15

Answer

9/17 > 3/15

Question 3 · pair 6

Compare 7/12 and 3/11 using one-half.

Steps only

7/12 > 1/2

3/11 < 1/2

7/12 > 3/11

Answer

7/12 > 3/11

Question 3 · pair 7

Compare 1/3 and 5/9 using one-half.

Steps only

1/3 < 1/2

5/9 > 1/2

1/3 < 5/9

Answer

1/3 < 5/9

Question 3 · pair 8

Compare 3/9 and 4/7 using one-half.

Steps only

3/9 < 1/2

4/7 > 1/2

3/9 < 4/7

Answer

3/9 < 4/7

Question Try This

Sixteen ants each have length 1/4 cm. What is their total length in a line without gaps?

Steps only

16 × 1/4 = 16/4

= 4 cm

Each whole is divided into 4 equal parts.

Answer

4 cm.

Question Fun with Relations

The only brother of your father’s sister has a child. How is that child related to you?

Steps only

Your father’s sister’s only brother is your father.

His child is you or your sibling.

Answer

It can be you; if it is another child, it is your sibling.