Converting a Fraction to a Percentage in a Real-World Situation

In this lesson, we solve real world problems involving conversion of fractions into percentages.

In a survey one in five people said they preferred a certain brand of fast food. Write this figure as a percentage.

Solution

Step 1:

The fraction of people preferring a certain brand of fast food = $\frac{1}{5}$

Step 2:

We multiply and divide the fraction by 20

$\frac{1}{5} = (1 \times 20) \div (5 \times 20) = \frac{20}{100}$

Step 3:

Writing this fraction as a percentage

By definition, $\frac{20}{100}$ = 20%

So, $\frac{1}{5}$ = 20%

Jamila is working out a problem involving $\mathbf{\frac{2}{3}}$. She needs to enter this fraction into a calculator. How would she enter $\mathbf{\frac{1}{4}}$ as a decimal on the calculator?

Solution

Step 1:

The fraction of people preferring a certain brand of fast food = $\frac{2}{3}$ On long division

$\frac{2}{3}$ = 0.6667

Step 2:

We multiply the decimal by 100

$0.6667 \times 100 = 66.67\%$

Step 3:

So, $\frac{2}{3}$ = 66.67%

In a clearance sale, a shop offers 30% off the original prices. What fraction is taken off the prices?

Solution

Step 1:

The percentage off on original prices in the shop = 30%

Step 2:

By definition of percent

30% = $\frac{30}{100} = \frac{3}{10}$

Step 3:

So, 30% = $\frac{3}{10}$