Solving Word Problems Involving Fractions

Problems involving fractions often appear in real-life situations.

Worked Example 9.1.1:

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  ×  breadth

= 30m × 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.

Worked Example 9.1.2:

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 methods.

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   = \( \frac{16}{24} \\ = \frac{2}{3}\)

Worked Example 9.1.3:

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 = ₦2,500

For food   =  ¹/₂  of ₦2,500

    = ¹/₂   ×   ₦2,500

        =      ₦1,250

For House rent  =   ¹/₄ of  ₦2,500

    =      ¹/₄     ×    N2,500

      =     ₦625.

For Transport = ¹/₁₀ of  ₦2,500

=  ¹/₁₀  × ₦2,500

= ₦250

Total spent = ₦1250 + ₦625 + ₦250

= ₦ 2,215

Miscellaneous    =   ₦2500    –    ₦2,125

= ₦375

ii. The fraction of the salary spent on miscellaneous is 

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