# Word Problems on Addition of Mixed Fractions

We will discuss here how to solve the word problems on addition of mixed fractions or addition of mixed numbers.

Let us consider some of the examples.

1. Sam bought 2 ½ kg of sugar from one shop and 6 2/3 kg of sugar from the other shop. How much sugar did he buy in all?

Solution:

Sugar bought from one shop = 2 ½ kg = 5/2 kg

Sugar bought from the other shop = 6 2/3 kg = 20/3 kg

Total quantity of sugar = 5/2 kg + 20/3 kg

= 5 × 3/2 × 3 kg + 20 × 2/3 × 2 kg, [L.C.M. of 2 and 3 = 6]

= 15/6 kg + 40/6 kg

= 55/6 kg

= 9 1/6 kg

So, Sam bought total 9 1/6 kg of sugar.

2. Mike bought 2 ½ kg of tomato, 1 3/8 kg of onion and 5 ¼ kg of brinjal. How much vegetables did he buy?

Solution:

Quantity of tomato Mike bought = 2 ½ kg

Quantity of onion he bought = 1 3/8 kg

Quantity of brinjal he bought = 5 ¼ kg

Total quantity of vegetables Mike bought = 2 ½ kg + 1 3/8 kg + 5 ¼ kg

= (2 + 1 + 5) + (1/2 + 3/8 + ¼) kg

= (8 + ½ + 3/8 + ¼) kg

= (8 + 1 × 4/2 × 4 + 3 × 1/8 × 1 + 1 × 2/4 × 2) kg, [L.C.M. of 2, 4 and 8 = 8]

= (8 + 4/8 + 3/8 + 2/8) kg

= (8 + 9/8) kg

= (8 + 1 1/8) kg

= (8 + 1 + 1/8) kg

= 9 1/8 kg

So, Mike bought total 9 1/8 kg of vegetables in all.

3. Ron walked 3 ¾ km on Monday, 4 1/3 km on Tuesday and 2 7/12 km on Wednesday. What distance did he walk in all?

Solution:

Distance Ron walked on Monday = 3 ¾ km

Distance he walked on Tuesday = 4 1/3 km

Distance he walked on Wednesday = 2 7/12 km

Total distance Ron walked = (3 ¾ + 4 1/3 + 2 7/12) km

= (15/4 + 13/3 + 31/12) km

= (15 × 3/ 4 × 3 + 13 × 4/3 × 4 + 31 × 1/12 × 1) km, [L.C.M. of 4, 3 and 12 = 12]

= (45/12 + 52/12 + 31/12) km

= 128/12 km

= 32/3 km

= 10 2/3 km

So, Ron walked total 10 2/3 km in all.

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