CAMBRIDGE PRIMARY

MATHEMATICS 0845

FRACTIONS and DECIMALS

STAGE 4 (GRADE 3)

• 4 Nn4 Use decimal notation and place value for tenths and hundredths in context , e.g. order

amounts of money; convert a sum of money such as $ 13.25 to cents , or a length such as 125 cm to

metres; round a sum of money to the nearest pound

• 4 Nn5 Understand decimal notation for tenths and hundredths in context e.g. length

• 4 Nn17 Order and compare two or more fractions with the same denominator (halves, quarters ,

thirds, fifths, eighths or tenths)

• 4 Nn18 Recognise the equivalence between : 1

2,

4

8, and

5

10,

1

4 and

2

8 ,

1

5 and

2

10

• 4 Nn19 Use equivalence to help order fractions , e.g. 7

10and

3

4

• 4 Nn20 Understand the equivalence between one-place decimals and fractions in tenths

• 4 Nn21 Understand that 1

2 is equivalent to 0.5 and also to

5

10

• 4 Nn22 Recognise the equivalence between the decimal fraction and vulgar fraction forms of halves,

quarters, tenths and hundredths

• 4 Nn23 Recognise mixed numbers, e.g. 53

4 , and order these on a number line

• 4 Nn24 Relate finding fractions to division

• 4 Nn25 Find halves , quarters, thirds, fifths, eighths and tenths of shapes and numbers

My sincere thanks to :

Ms Preeti Kaushik,our art teacher for designing and editing this unit

Ms Shruti Verma for maintaining the blog

Mr Madan Saini for reviewing this unit

Suresh Goel

(Director)

Alliance World School

Noida , Delhi-NCR, India

Fractions and Decimals P-1

• Decimal Notation for tenths :

1 Centimetre = 10 Millimetre

( 1 cm = 10 mm )

Thickness of a Sharpener = 6 mm = 6

10 = 0.6 cm ( Zero point six cm)

Length of a paper clip 3 cm and 4 mm = 34

10 cm = 3.4 cm ( Three point four cm)

Length of pencil = 7 cm and 5 mm = 7 5

10 cm = 7.5 cm ( Seven point five cm)

4Nn5

Decimal Point

One tenth 𝟏

𝟏𝟎 = 0 . 1

0.1 is read as "zero point one"

1 cm = 10 mm

or 1mm = 𝟏

𝟏𝟎 cm

= 0.1 cm

1 millimetre 1 centimetre

10 millimetre

Fractions and Decimals P-2

Exercise - 1

a) Write the following measures in cm ( using decimal )

(i) 5mm

(ii) 26 mm = 20mm + 6 mm = 2 6

10 cm = 2.6 cm (done for you)

(iii) 7cm and 8 mm

(iv) 127 mm

b) Write the numbers in part (a) in the place value chart :

2 6

c) Write the following measures in mm.

(i) 2.5 cm

(ii) 0.7 cm

(iii) 20.4 cm

(iv) 13.5 cm

Place Value Chart

(ii)

(iii)

(iv)

(i)

(ii)

(iii)

(iv)

4Nn5

Fractions and Decimals P-3

• Decimal Notation for hundredths :

1 metre = 100 centimetre ( 1 m = 100 cm)

(a) Breadth of a pencil box = 8 cm = 8

100 m = 8 hundredths m = 0.08 m

(b) Length of a note book = 29 cm = 29

100 m = 29 hundredths m = 0.29 m

(c) Length of a ruler = 30cm = 30

100 m = 30 hundredths m = 0.30 m

(d) Length of class room = 3m 57cm = 357

100 m = 3. 57 m

Decimal Point

One hundredth 𝟏

𝟏𝟎𝟎 = 0 . 01

0.01 is read as "zero point zero one"

1 metre = 100 cm

1 cm = 1

100 m

= one hundredth m

1 cm = 0.01 m

0.1 = 0.10

or

1tenth = 10 hundredths

4Nn5

Fractions and Decimals P-4

Exercise - 2

(a) write the following measures in meters ( using decimal)

i. 7cm

ii. 28 cm = 28

100 m = 0.28 m (Done for you)

iii. 107cm = ( 100 + 7)𝑐𝑚 = 17

100 𝑚 = 1.07 𝑚 (Done for you)

iv. 543cm

v. 3 m 41 cm

vi. 37 cm

(b) Write the number in part (a) in the place value chart

i

ii 0 2 8

iii 1 0 7

iv

v

vi

(c) Write the following measures in cm :

i. 3.67 cm = 367

100 = 3m 67 cm = (300+ 67) cm = 367 cm (done for you)

ii. 0.05 m

iii. 1.30 m

iv. 2.01 m

Place Value Chart

4Nn5

Fractions and Decimals P-5

$ 1 = 100 cents

or 1 cent = $ 𝟏

𝟏𝟎𝟎

one hundredth of a $ = $ 0.01

Exercise -3

(a) Convert the amount of money to cents :

i. $ 13.25 = $ 1325

100 = $ 13 and 25 cents = (1300 + 25) cents = 1325 cents

(done for you)

ii. $ 15.30

iii. $0.37

iv. $ 0.04 = $ 4

100 = 4 cents (done for you)

v. $ 5.57

(b) Write the numbers in part (a) in the place value chart :

( i) 1 3 2 5

(ii)

(iii)

(iv) 0 0 4

(v)

(c) Convert the amount of money to dollars (using decimal point) :

i. 37 cents ii. 5 cents iii. 102 cents

iv. 1206 cents v. 1537 cents

4Nn4

0.1 = 0.10 or one tenth = 10 hundredths

Place Value Chart

Fractions and Decimals P-6

Fractions are several parts of whole

Example:

The shaded part is three seventh of the whole.

Written as 𝟑

𝟕

• The number 7 below the division line is called denominator of the

fraction and it denotes that one whole is being divided in seven equal parts.

• The number 3 above the division line is called numerator of the

fraction and it denotes the number of parts taken in the fraction.

Exercise - 4

• Order the fractions from the smallest to the largest:

i) 𝟓

𝟐 ,

𝟏

𝟐 , 𝟐 ,

𝟗

𝟐

0 𝟏

𝟐 1

𝟑

𝟐 2 3 4 5

𝒊 . 𝟏

𝟐 <

𝟒

𝟐 <

𝟓

𝟐 <

𝟗

𝟐 ( 𝒏𝒐𝒕𝒆 ∶ 𝟐 =

𝟒

𝟐) (done for you)

𝒊𝒊 . 𝟑

𝟒 ,

𝟏

𝟒 , 𝟐 ,

𝟕

𝟒 ,

𝟏

𝟐

𝒊𝒊𝒊 . 𝟏

𝟓 , 𝟏 ,

𝟏𝟑

𝟓 ,

𝟒

𝟓

𝒊𝒗 . 𝟖

𝟑 ,

𝟐

𝟑 , 𝟑 ,

𝟒

𝟑

𝒗 . 𝟐

𝟖 ,

𝟏

𝟐 , 𝟏 ,

𝟑

𝟒

𝒗𝒊 . 𝟑

𝟏𝟎 ,

𝟑

𝟓 ,

𝟏

𝟐 ,

𝟕

𝟏𝟎

4Nn17

• " Is greater than" is denoted by the symbol >

• "Is less than" is denoted by the symbol <

Example : i. 5 > 2 , ii. 3 < 7

If we are given two or more fractions with the

same denominator, then the fraction with greater

numerator is greater.

Fractions and Decimals P-7

• Equivalence of Fractions :

( a ) 𝟏

𝟐 One half

𝟒

𝟖 Four eights

𝟓

𝟏𝟎 Five tenths

hence 𝟏

𝟐 =

𝟒

𝟖 =

𝟓

𝟏𝟎

(b)

1 whole

𝟏

𝟒 one quarter

𝟏

𝟒 =

𝟏×𝟐

𝟒×𝟐 =

𝟐

𝟖

𝟐

𝟖 two eighths or

𝟏

𝟒 =

𝟐

𝟖

(c)

𝟏

𝟓 𝒐𝒏𝒆 𝒇𝒊𝒇𝒕𝒉

𝟏

𝟓 =

𝟏×𝟐

𝟓×𝟐 =

𝟐

𝟏𝟎

𝟐

𝟏𝟎 𝒕𝒘𝒐 𝒕𝒆𝒏𝒕𝒉𝒔 𝐨𝐫

𝟏

𝟓 =

𝟐

𝟏𝟎

4Nn18

1 Whole

1

2=

1 × 4

2 × 4=

4

8

1

2=

1 × 5

2 × 5=

5

10

If we multiply the numerator and the

denominator by the same number, we

get another fraction equivalent to the

given fraction.

Example :

Fractions and Decimals P-8

EXERCISE - 5

• Order the following fractions :

(a) 7

10 and

3

4 Multiples of 10 = 10,20,30,....

7

10 =

7×2

10×2 =

14

20 ...(i) [as 20 ÷ 10 = 2] Multiples of 4 = 4,8,12,16,20, 24, ..

3

4 =

3×5

4×5 =

15

20 ... (ii) [as 20 ÷ 4 = 5] Common multiple of 10 and 4 = 20

14

20 <

15

20 ( from (i) and (ii) )

or 𝟕

𝟏𝟎 <

𝟑

𝟒 (done for you)

(b)

2

5 and

1

3 Multiples of 5 = 5, 10,15, 20,....

2

5 =

2×3

5×3 =

6

15 ... (i) [as 15 ÷ 5 = 3] Multiples of 3 = 3, 6, 9, 12, 15, 18, ....

1

3 =

1×5

3×5 =

5

15 ...(ii) [as 15 ÷ 3 = 5] Common multiple of 5 and 3 = 15

6

15 >

5

15 ( from (i) and (ii) )

or 𝟐

𝟓 >

𝟏

𝟑 (done for you)

(c) 2

3 and

5

6

(d) 4

7 and

3

4

(e) 9

10 and

6

7

(f) 3

8 and

5

12

Order of fractions :

Find equivalent fractions with a

common denominator and compare.

4Nn19

Fractions and Decimals P-9

• Equivalence between decimal fractions and vulgar fractions

0.25

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 𝟏

𝟏𝟎

𝟐

𝟏𝟎

𝟑

𝟏𝟎

𝟒

𝟏𝟎

𝟓

𝟏𝟎

𝟔

𝟏𝟎

𝟕

𝟏𝟎

𝟖

𝟏𝟎

𝟗

𝟏𝟎 𝟏

𝟏

𝟐=

𝟏×𝟓

𝟐×𝟓=

𝟓

𝟏𝟎= 𝟓 𝒕𝒆𝒏𝒕𝒉𝒔 = 𝟎. 𝟓 as 10 ÷ 2 = 5

𝟏

𝟒=

𝟏×𝟐𝟓

𝟒×𝟐𝟓=

𝟐𝟓

𝟏𝟎𝟎= 𝟐𝟓 𝒉𝒖𝒏𝒅𝒓𝒆𝒅𝒕𝒉𝒔 = 𝟎. 𝟐𝟓 as 100 ÷ 4 = 25

Exercise - 6

(a) Express the following fractions in decimals :

i) 𝟐

𝟓

ii) 𝟑

𝟐𝟎

iii) 𝟑

𝟒

iv) 𝟕

𝟐𝟓

(b) Express the following decimals to fractions / mixed fractions :

i) 0.05

ii) 0.5

iii) 5.6

iv) 30.01

4Nn20- 22

Fractions and Decimals P-10

Exercise - 7

Represent the following mixed numbers on the number line and order these

numbers:

(i) 53

4 , 4

1

2 , 3

1

8 , 1

1

4

11

4 3

1

8 4

1

2 5

3

4

0 1 2 3 4 5 6

𝟓𝟑

𝟒= 𝟓 𝒘𝒉𝒐𝒍𝒆 𝒂𝒏𝒅 𝟑 𝒒𝒖𝒂𝒓𝒕𝒆𝒓𝒔

𝟒𝟏

𝟐= 𝟒 𝒘𝒉𝒐𝒍𝒆 𝒂𝒏𝒅 𝒐𝒏𝒆 𝒉𝒂𝒍𝒇 = 𝟒 𝒘𝒉𝒐𝒍𝒆 𝒂𝒏𝒅 𝟐 𝒒𝒖𝒂𝒓𝒕𝒆𝒓 (

𝟏

𝟐=

𝟐

𝟒)

𝟑𝟏

𝟖= 𝟑 𝒘𝒉𝒐𝒍𝒆 𝐚𝐧𝐝 𝐨𝐧𝐞 𝐞𝐢𝐠𝐡𝐭𝐡 = 𝟑 𝐰𝐡𝐨𝐥𝐞 𝐚𝐧𝐝 𝐛𝐞𝐭𝐰𝐞𝐞𝐧 𝟑 𝐚𝐧𝐝 𝟏 𝐪𝐮𝐚𝐫𝐭𝐞𝐫

𝟏𝟏

𝟒= 𝟏 𝒘𝒉𝒐𝒍𝒆 𝒂𝒏𝒅 𝟏 𝒒𝒖𝒂𝒓𝒕𝒆𝒓

𝟏𝟏

𝟒 < 3

𝟏

𝟖 < 4

𝟏

𝟐 < 5

𝟑

𝟒

(ii) 𝟐𝟐

𝟏𝟎 , 𝟏

𝟏

𝟓 , 𝟒

𝟏

𝟐 , 𝟓

𝟑

𝟒

(iii) 1𝟐

𝟑 , 𝟐

𝟓

𝟔 , 𝟒

𝟏

𝟑 , 𝟓

𝟏

𝟔

(iv) 𝟏𝟏

𝟐 ,

𝟓

𝟒 ,

𝟕

𝟖 , 𝟑

𝟏

𝟒

4Nn23

Fractions and Decimals P-11

Exercise - 8

(a) Find halves of the following numbers :

(𝑖) 1

2 𝑜𝑓 12 = 𝟏𝟐 ÷ 𝟐 = 𝟔 𝑎𝑠 2 × 6 = 12 (done for you)

(𝑖𝑖) 1

2 𝑜𝑓 16 (𝑖𝑖𝑖)

1

2 𝑜𝑓 20 (𝑖𝑣)

1

2 𝑜𝑓 10

(b) Find thirds of the following numbers :

(𝑖) 1

3 𝑜𝑓 12 = 𝟏𝟐 ÷ 𝟑 = 𝟒 𝑎𝑠 3 × 4 = 12 (done for you)

(𝑖𝑖) 1

3 𝑜𝑓 15 (𝑖𝑖𝑖)

1

3 𝑜𝑓 24 (𝑖𝑣)

1

3 𝑜𝑓 30

(c) Find quarters of the following numbers :

(𝑖) 1

4 𝑜𝑓 12 = 𝟏𝟐 ÷ 𝟒 = 𝟑 𝑎𝑠 4 × 3 = 12 (done for you)

(𝑖𝑖) 1

4 𝑜𝑓 16 (𝑖𝑖𝑖)

1

4 𝑜𝑓 24 (𝑖𝑣)

1

4 𝑜𝑓 40

(d) Find fifths of the following numbers :

(𝑖) 1

5 𝑜𝑓 15 = 𝟏𝟓 ÷ 𝟓 = 𝟑 𝑎𝑠 5 × 3 = 15 (done for you)

(𝑖𝑖) 1

5 𝑜𝑓 30 (𝑖𝑖𝑖)

1

5 𝑜𝑓 40 (𝑖𝑣)

1

5 𝑜𝑓 50

(e) Find eighths of the following numbers :

(𝑖) 1

8 𝑜𝑓 16 = 𝟏𝟔 ÷ 𝟖 = 𝟐 𝑎𝑠 8 × 2 = 16 (done for you)

(𝑖𝑖) 1

8 𝑜𝑓 24 (𝑖𝑖𝑖)

1

8 𝑜𝑓 32 (𝑖𝑣)

1

8 𝑜𝑓 80

(f) Find tenths of the following numbers :

(𝑖) 1

10 𝑜𝑓 20 = 𝟐𝟎 ÷ 𝟏𝟎 = 𝟐 𝑎𝑠 10 × 2 = 20 (done for you)

(𝑖𝑖) 1

10 𝑜𝑓 50 (𝑖𝑖𝑖)

1

10 𝑜𝑓 70 (𝑖𝑣)

1

10 𝑜𝑓 100

4Nn24

Fractions and Decimals P-12

Exercise - 9

(a) Find the quarters of the following numbers :

(𝑖) 3

4 𝑜𝑓 24 = 3 𝑡𝑖𝑚𝑒𝑠 (

1

4 𝑜𝑓 24 ) = 3 𝑡𝑖𝑚𝑒𝑠 (24 ÷ 4) = 3 × 6 = 18

(done for you)

(𝑖𝑖) 2

4 𝑜𝑓 16 (𝑖𝑖𝑖)

1

4 𝑜𝑓 36 (𝑖𝑣)

3

4 𝑜𝑓 40

(b) Find the thirds of the following numbers :

(𝑖) 2

3 𝑜𝑓 36 = 2 𝑡𝑖𝑚𝑒𝑠 (

1

3 𝑜𝑓 36 ) = 2 𝑡𝑖𝑚𝑒𝑠 (36 ÷ 3) = 2 × 12 = 24

(done for you)

(𝑖𝑖) 1

3 𝑜𝑓 27 (𝑖𝑖𝑖)

2

3 𝑜𝑓 12 (𝑖𝑣)

1

3 𝑜𝑓 18

(c) Find the fifths of the following numbers :

(𝑖) 3

5 𝑜𝑓 25 = 3 𝑡𝑖𝑚𝑒𝑠 (

1

5 𝑜𝑓 25 ) = 3 𝑡𝑖𝑚𝑒𝑠 (25 ÷ 5) = 3 × 5 = 15

(done for you)

(𝑖𝑖) 2

5 𝑜𝑓 40 (𝑖𝑖𝑖)

1

5 𝑜𝑓 35 (𝑖𝑣)

3

5 𝑜𝑓 20

(d) Find the eighths of the following numbers :

(𝑖) 5

8 𝑜𝑓 40 = 5 𝑡𝑖𝑚𝑒𝑠 (

1

8 𝑜𝑓 40 ) = 5 𝑡𝑖𝑚𝑒𝑠 (40 ÷ 8) = 5 × 5 = 25

(done for you)

(𝑖𝑖) 3

8 𝑜𝑓 32 (𝑖𝑖𝑖)

7

8 𝑜𝑓 56 (𝑖𝑣)

2

8 𝑜𝑓 48

(e) Find the tenths of the following numbers :

(𝑖) 7

10 𝑜𝑓 30 = 7 𝑡𝑖𝑚𝑒𝑠 (

1

10 𝑜𝑓 30) = 7 𝑡𝑖𝑚𝑒𝑠 (30 ÷ 10) = 7 × 3 = 21

(done for you)

(𝑖𝑖) 3

10 𝑜𝑓 40 (𝑖𝑖𝑖)

9

10 𝑜𝑓 50 (𝑖𝑣)

5

10 𝑜𝑓 60

4Nn25

Fractions and Decimals P-13

Exercise - 10

(a) Shade halves of the following shapes :

i. ii.

iii. iv.

(b) Shade quarters of the following shapes :

i. ii.

shade 𝟑

𝟒th shade

𝟑

𝟒th shade

𝟐

𝟒th

iii. iv.

shade 𝟏

𝟒th shade

𝟏

𝟒th

4Nn25

Fractions and Decimals P-14

(c) Shade thirds of the following shapes :

i. ii.

shade 𝟏

𝟑rd shade

𝟐

𝟑rd

iii. iv.

shade 𝟏

𝟑rd shade

𝟐

𝟑rd

(d) Shade fifths of the following shapes :

i. ii.

shade 𝟑

𝟓th shade

𝟏

𝟓th

iii. iv.

shade 𝟐

𝟓th shade

𝟒

𝟓th

4Nn25

Fractions and Decimals P-15

(e) Shade eights of the following shapes :

i. ii.

shade 𝟓

𝟖th shade

𝟑

𝟖th

iii. iv.

shade 𝟐

𝟖th shade

𝟕

𝟖th

(f) Shade tenths of the following shapes :

i. ii.

shade 𝟓

𝟏𝟎th shade

𝟐

𝟏𝟎th

iii. iv.

shade 𝟑

𝟏𝟎th shade

𝟕

𝟏𝟎th

4Nn25