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# Addition and Subtraction of Mixed Fractions

In a joint family of Saravanan, during pongal festival celebration, his grandfather, his father and himself wanted to wear the same colour shirt.

Addition and Subtraction of Mixed Fractions

Think about the situation

In a joint family of Saravanan, during pongal festival celebration, his grandfather, his father and himself wanted to wear the same colour shirt. The cloth needed for stitching 3 shirts are 2 3/4 m, 2 1/2 m and 1 1/4 m respectively. How many metres of cloth has to be purchased in total?

So the total length of the cloth bought by his father is 2 3/4 + 2 1/2 +1 1/4 . This is solved in the following example.

Example 12

Saravanan’s father bought 2 3/4 m , 2 1/2 m and 1 1/4 m  of cloth. Find the total  length of the cloth bought by him?

Solution

Example 13

Add: 3 2/4 + 7 2/5

Solution 3 2/4 + 7 2/5 = 3 + 2/4 + 7 + 2/5

= 3 + 7 + (2/4 + 2/5)

= 10 + (10/20 + 8/20)

= 10 + 18/20 = 10 + 9/10 =10 9/10

Think about the situation

One day Anitha’s mother bought 5 1/2 litres of milk. She has used only 3 1/4 litres of milk to prepare payasam. How much milk is left? That is 5 1/2 – 3 1/4.

Example 14

In the above situation, find the quantity of milk left over. So, subtract 3 1/4 from 5 1/2

Solution

The quantity of milk left over = 5 1/2 − 3 1/4

Here, note that 5 > 3 and 1/2 > 1/4

The whole numbers 5 and 3 and the fractional numbers 1/2 and 1/4 can be subtracted separately.

So 5 ½ − 3 ¼ = (5 – 3) + (1/2 – 1/4)

= 2 + (2/4 -1/4) (Since the equivalent fraction of 1/2 is 2/4)

= 2 + 1/4 = 2 1/4 liters

Note

This method is applicable only when both integral and fractional parts of minuend is greater than that of the subtrahend.

Example 15

Simplify: 9 1/4 − 3 5/6

Solution

Here 9 > 3 and 1/4 < 5/6, So we proceed as follows:

We convert the mixed fraction into improper fraction and then subtract.

9 1/4 = [(9 × 4) + 1] / 4 = 37 / 4

And 3 5/6 = [(3 × 6) + 5] / 6 = 23/6

Common multiple of 4 and 6 is 12.

Now, 37/4 – 23/6 = [37 × 3] /12 – [23 × 2] / 12

= 111/12 – 46/12 = 65/12 = 5 5/12

Try these

i) Find the sum of 5 4/9 and 3 1/6

5 4/9 + 3 1/6

49/9 + 19/6

[98 + 57] / 18 = 155/18

= 8 11/18

ii) Subtract 7 1/6 from 12 3/8.

12 3/8 – 7 1/6

99/8 – 43/6

[297 – 172] / 24 = 125/24

= 5 5/24

iii) Subtract the sum of 6 1/6 and 3 1/5 from the sum of 9 2/3 and 2 1/2.

= (9 2/3 + 2 1/2) – (6 1/6 + 3 1/5 )

= ( 29/3 + 5/2) – ( 37/6 + 16/5)

= ( 58 + 15/6) – ( 185 + 96/30)

= 73/6 – 281/30

= 365 – 281/30 = 84/30 = 2  24/30 = 2 4/5

Tags : Fractions | Term 3 Chapter 1 | 6th Maths , 6th Maths : Term 3 Unit 1 : Fractions
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6th Maths : Term 3 Unit 1 : Fractions : Addition and Subtraction of Mixed Fractions | Fractions | Term 3 Chapter 1 | 6th Maths