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.

**Related Concept**

● Representation of a Fraction

● Properties of Equivalent Fractions

● Comparison of Like Fractions

● Comparison of Fractions having the same Numerator

● Conversion of Fractions into Fractions having Same Denominator

● Conversion of a Fraction into its Smallest and Simplest Form

● Addition of Fractions having the Same Denominator

● Subtraction of Fractions having the Same Denominator

● Addition and Subtraction of Fractions on the Fraction Number Line

**4th Grade Math Activities**

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