Percentages (VCE SSCE General Mathematics): Revision Notes

Worked Example: Converting a Fraction to a Percentage

Convert $\frac{36}{90}$ to a percentage.

Solution:

Multiply the fraction by $100$:

$\frac{36}{90} \times 100 = 40\%$

Therefore, $\frac{36}{90}$ expressed as a percentage is $40\%$.

Worked Example: Converting a Decimal to a Percentage

Convert $0.75$ to a percentage.

Solution:

Multiply by $100$:

$0.75 \times 100 = 75\%$

Worked Example: Converting a Percentage to a Fraction

Convert $62\%$ to a fraction.

Solution:

Since $62\%$ means sixty-two out of one hundred:

$62\% = \frac{62}{100}$

Simplify by dividing both numerator and denominator by $2$:

Worked Example: Converting a Percentage to a Decimal

Convert $72\%$ to a decimal.

Solution:

Write $72\%$ as a fraction out of $100$:

$\frac{72}{100} = 0.72$

Worked Example: Finding a Percentage of a Quantity

Find $15\%$ of $140.

Solution:

Write out the problem with $15\%$ as a fraction:

$15\% \text{ of } 140 = \frac{15}{100} \text{ of } 140$

Change "of" to multiply:

$= \frac{15}{100} \times 140$

Calculate:

$= 21$

Therefore, $15\%$ of $140 is $21.

Worked Example 1: Comparing Quantities with Same Units

There are $18$ girls in a class of $25$ students. What percentage of the class are girls?

Solution:

Work out the fraction of girls:

$\text{Girls} = \frac{18}{25}$

Convert to a percentage by multiplying by $100$:

$\frac{18}{25} \times 100 = 72$

Therefore, 72% of the class are girls.

Worked Example 2: Comparing Quantities with Different Units

Express $76$ mm as a percentage of $40$ cm.

Solution:

First, convert $40$ centimetres to millimetres. Since there are $10$ millimetres in $1$ centimetre:

$40 \text{ cm} = 40 \times 10 = 400 \text{ mm}$

Now both quantities are in millimetres. Write $76$ mm as a fraction of $400$ mm:

$\frac{76}{400}$

Multiply by $100$ to convert to a percentage:

$\frac{76}{400} \times 100 = 19\%$