In this lesson, we are solving real world problems related to conversion between percentages and decimals.
Lizzy bought some fabric that was 1.75 meters long. How could this be written as a fraction?
Step 1:
To convert the decimal to a fraction we multiply and divide by 100
$1.75 = \left ( \frac{1.75}{100} \right) \times 100 = \frac{(1.75 \times 100)}{100} = \frac{175}{100}$
Step 2:
Reducing to lowest terms
$\frac{175}{100} = \frac{7}{4}$
So, 1.75 = $\frac{7}{4}$
Kylie pays tax at the rate of 25% of her income. What fraction of Kylie’s income is this?
Step 1:
By definition of a per cent, for any whole number x, x% = $\frac{x}{100}$
Step 2:
To convert the percentage to a fraction, from definition x% = $\frac{x}{100}$.
25% = $\frac{25}{100}$
Reducing to lowest terms
$\frac{25}{100} = \frac{1}{4}$
So, 25% = $\frac{1}{4}$
Laura bought a coat in the January sales with $\mathbf{ \frac{1}{5}}$ off the original price. What percentage was taken off the price of the coat?
Step 1:
The fraction off the original price = $\frac{1}{5}$
Step 2:
To convert the fraction to percentage, multiply and divide it by 20
$\frac{(1 \times 20)}{(5 \times 20)} = \frac{20}{100}$
Step 3:
By definition of percentage
$\frac{20}{100}$ = 20%
So, $\frac{1}{5}$ = 20%