Lesson 9, Topic 1
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# Solving Word Problems Involving Fractions

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Problems involving fractions often appear in real-life situations.

Example 1

The length of a field is 30m and the breadth is 20m. Calculate $$\frac{1}{10}$$of the area of the field.

Solution

Area of the field = length  x  breadth

= 30m x 20m

= 600m2

Hence,  $$\frac {1}{10} \scriptsize \: of \: 600m^2$$

=$$\frac {1}{10} \scriptsize \: \times \: 600m^2$$

= 60m2

Therefore, $$\frac{1}{10}$$ of the area of the field is 60m2.

Example 2

A loaf of bread was divided into 24 equal sides. If 8 slices were given to Segun, what fraction is left?

Solution

This question can be solved using two different method.

Method 1

Let the whole loaf of bread be 1.

Since 8 out of 24 was given out, so this represents $$\frac{8}{24}$$ of the total.

The amount left    = $$\scriptsize 1\: -\: \normalsize \frac{8}{24}$$

Note: $$\frac{24}{24} \scriptsize = 1$$

$$\scriptsize 1\: – \: \normalsize \frac {8}{24}\\ = \frac{24}{24}\: – \: \frac{8}{24} \\ = \frac{16}{24} \\ = \frac{2}{3}$$

The fraction left is $$\frac{2}{3}$$

Method 2

The original loaf has 24 slices. Since 8 slices were given to Segun, the remaining slices  =  24   –  8   =  16.

The fraction left   = $$\frac{16}{24} \\ = \frac{2}{3}$$

Example 3

Mr. Oladele received N2,500 as his salary last month. He spent 1/2 of it on food, 1/4 on house rent, 1/10 on transport, and the rest on miscellaneous things.

i. Find the amount he spent on each of these items?

ii. What fraction of his salary was spent on miscellaneous things?

Solution

i. Total amount received = N2,500

For food   =  1/2  of N2,500

= 1/2     x   N2,500

=      N1,250

For House rent    =   1/4 of   N2,500

=      1/4     x      N2,500

=     N625.

For Transport = 1/10 of   N2,500

=  1/10  x N2,500

= N250

Total spent = N1250 + N625 + N250

= N 2,215

Miscellaneous    =   N2500    –    N2,125

= N375

ii. The fraction of the salary spent on miscellaneous is

= $$\frac{375}{2500} \\ = \frac{75}{100} \\ = \frac{15}{100} \\ = \frac{3}{20}$$ error: