# Evaluate Fractions of Quantities

Examples on evaluating fractions of quantities and questions and their solutions are presented.

## Examples with Solutions

   

Example 1
What is $\displaystyle \frac{2}{5}$ of $500$ ?

Solution to Example 1

$\displaystyle \frac{2}{5}$ of $500$ is written as $\displaystyle \frac{2}{5} \times 500$ and evaluate as follows $\displaystyle \frac{2}{5} \times 500 = \frac{2 \times 500}{5} = \frac{1000}{5} = 1000 \div 5 = 200$

Example 2
What is $\displaystyle \frac{3}{7}$ of $700$?

Solution to Example 2

$\displaystyle \frac{3}{7}$ of $700$ is written as $\displaystyle \frac{3}{7} \times 700$ and evaluate as follows $\displaystyle \frac{3}{7} \times 700 = \frac{3 \times 700}{7} = 2100 \div 7 = 300$

Example 3
Express $\displaystyle \frac{3}{8}$ of 1 Kg in grams?

Solution to Example 3

1 Kg = 1000 g
Hence $\displaystyle \frac{3}{8}$ of 1 Kg is written as $\displaystyle \frac{3}{8} \times 1 \; \text{Kg}$ Substitute 1 Kg by 1000 g $= \displaystyle \frac{3}{8} \times 1000 \; \text{g}$ and evaluate as follows $= \frac{3 \times 1000}{8} = 3000 \div 8 = 375 \; \text{g}$

Example 4
There are 900 holidaymakers in a hotel. One third of these holidaymakers are from Germany. One third of those not from Germany are from the UK. How many holidaymakers from the UK are staying at the hotel?

Solution to Example 4

The number of holidaymakers from Germany is given by $\displaystyle \frac{1}{3} \times 900$ evaluate to obtain. $= \frac{1 \times 900}{3} = 300 \;$ The number of holidaymakers from Germany is equal to 300.
The number of of holidaymakers NOT from Germany is given by $900 - 300 = 600$ One third of those not from Germany are from the UK. Therefore, the number of holidaymakers from the UK is given by $\displaystyle \frac{1}{3} \times 600$ evaluate to obtain $= \displaystyle \frac{600}{3} = 200$ 200 holidaymakers are from the UK.

## Questions with Solutions

Evaluate the following:

1. $\displaystyle \frac{1}{10}$ of 2500 people

2. $\displaystyle \frac{2}{4}$ of 1.02 grams

3. $\displaystyle \frac{3}{5}$ of 1000 students

4. $\displaystyle \frac{1}{9}$ of 270 cars

## Solutions to the Exercises

1. $\displaystyle \frac{1}{10}$ of 2500 people = $\displaystyle \frac{1}{10} \times 2500 = \frac{1 \times 2500}{10} = 250$ people

2. $\displaystyle \frac{2}{4}$ of 1.02 grams = $\displaystyle \frac{2}{4} \times 1.02 = \frac{2 \times 1.01}{4} = 0.505$ grams

3. $\displaystyle \frac{3}{5}$ of 1000 students = $\displaystyle \frac{3}{5} \times 1000 = \frac{3 \times 1000}{5} = 600$ students

4. $\displaystyle \frac{1}{9}$ of 270 cars = $\displaystyle \frac{1}{9} \times 270 = \frac{1 \times 270}{9} = 30$ cars