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

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 \[ = \frac{3 \times 1000}{8} = 3000 \div 8 = 375 \; \text{g} \]

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.

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.

Evaluate the following:

- \( \displaystyle \frac{1}{10} \) of 2500 people

- \( \displaystyle \frac{2}{4} \) of 1.02 grams

- \( \displaystyle \frac{3}{5} \) of 1000 students

- \( \displaystyle \frac{1}{9} \) of 270 cars

- \( \displaystyle \frac{1}{10} \) of 2500 people = \( \displaystyle \frac{1}{10} \times 2500 = \frac{1 \times 2500}{10} = 250 \) people

- \( \displaystyle \frac{2}{4} \) of 1.02 grams = \( \displaystyle \frac{2}{4} \times 1.02 = \frac{2 \times 1.01}{4} = 0.505 \) grams

- \( \displaystyle \frac{3}{5} \) of 1000 students = \( \displaystyle \frac{3}{5} \times 1000 = \frac{3 \times 1000}{5} = 600 \) students

- \( \displaystyle \frac{1}{9} \) of 270 cars = \( \displaystyle \frac{1}{9} \times 270 = \frac{1 \times 270}{9} = 30 \) cars

- Fractions and Mixed Numbers
- Equivalent Fractions
- Reduce Fractions
- Adding Fractions
- Fraction Multiplication
- Fraction Division
- Complex Fractions with Variables
- Greatest Common Factor
- Lowest Common Multiple
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