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 Â xÂ breadth

= 30mÂ x 20m

= 600m^{2}

Hence,Â \(\frac {1}{10} \scriptsize \: of \: 600m^2\)

Â =\(\frac {1}{10} \scriptsize \: \times \: 600m^2\)

= 60m^{2}

Therefore, \(\frac{1}{10}\) of the area of the field is 60m^{2}.

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 leftÂ Â =Â \( \scriptsize 1\: -\: \normalsize \frac{8}{24} \)

** Note: **\( \frac{24}{24} \scriptsize = 1 \)

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 Â =Â 24 Â –Â 8 Â =Â 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

Â Â = ^{1}/_{2}Â Â Â x Â 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 isÂ

= \(\frac{375}{2500} \\ = \frac{75}{100} \\ = \frac{15}{100} \\ = \frac{3}{20}\) Â