This topic will focus on the various types of word problems on addition, subtraction, multiplication and division. Previously we have dealt with each of them separately. This topic will provide sums from different domains of fraction involving the four basic operation and we need to understand the sum given and then decide which basic operation to follow. Hence it will require more in-depth understanding of the topic in detail.

Here are few examples on word problem of fraction.

**1.** Rohit purchased 31/4 kgs of potatoes, 51/2 kgs of tomatoes and 41/5 kgs of other vegetables. Find the total kgs of vegetables brought by Rohit.

**Solution:**

Quantity of potatoes purchased = 31/4 kg

Quantity of tomatoes purchased = 51/2 kg

Quantity of other vegetables purchased = 41/5 kg

Total quantity of vegetables purchased = 31/4 + 51/2 + 41/5

= 13/4 + 11/2 + 21/5

= (65+110+84)/20

= 259/20

= 12 19/20 kgs.

In the sum the quantity of potatoes, tomatoes and other vegetables purchased are given. We have to add all the quantities to get the total quantity of vegetables purchased.

**2.** Leena had 506/5 m of cloth. She has used 306/7 m of cloth for her craft work. Find how much length of cloth is left?

**Solution:**

Total length of cloth Leena had = 506/5 m

Length of cloth used for her craft = 306/7 m

Length of cloth left = 506/5 – 306/7

= 256/5 – 216/7

= (256 ×7 ̶ 216 × 5)/35

= (1792 ̶1080)/35

= 712/35

= 20 12/35 m

It is mentioned in the sum that Leena purchased certain length of cloth and she used a certain length of cloth for her craft. So, we have to subtract them to get the length of cloth left.

**3.** There are 50 mangoes and Ram and his brother ate 3/5 of the mangoes. Find the number of mangoes left.

**Solution:**

Total number of mangoes = 50

Fraction of mangoes ate by Ram and his brother = 3/5

Therefore, fraction of mangoes ate by Ram and his brother = 50 × 3/5

= 30

Hence, no. of mangoes left = 50 – 30 = 20 mangoes

It is mentioned in the sum that there are 50 mangoes. Ram and his brother ate a certain fraction of it. So we will have to multiply that fraction with total no. of mangoes to get the number of mangoes ate by Ram and his brother.

**4.** There are 800 boys in a school. The fraction of girls in the school is 2/3. Find the number of girls in the school.

**Solution:**

Let the total no. of students be 1

Fraction of girls = 2/3

Fraction of boys = 1 – 2/3

= 1/3

Therefore 1/3 of the students are boys = 800

Then total no. of students = 800 ÷ 1/3

= 800 × 3/1

= 2400 students

Therefore, number of girls = 2400 – 800 = 1600 girls

It is mentioned that in a school there are 800 boys and the fraction of girls is given. The whole fraction is always considered as 1. Hence the fraction of boys is calculated by subtracting the fraction of girls from the total fraction (1). Then on dividing the number of boys by the fraction of boys we get the total number of students and can then easily find out the number of girls.

**From Worksheet on Simplification of Fractions to HOME PAGE**

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