Converting Between Percentages and Decimals in a Real-World Situation

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?

Solution

Step 1:

To convert the decimal to a fraction we multiply and spanide by 100

$1.75 = left ( frac{1.75}{100} ight) imes 100 = frac{(1.75 imes 100)}{100} = frac{175}{100}$

Step 2:

Reducing to lowest terms

$frac{175}{100} = frac{7}{4}$

So, 1.75 = $frac{7}{4}$

Kype pays tax at the rate of 25% of her income. What fraction of Kype’s income is this?

Solution

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?

Solution

Step 1:

The fraction off the original price = $frac{1}{5}$

Step 2:

To convert the fraction to percentage, multiply and spanide it by 20

$frac{(1 imes 20)}{(5 imes 20)} = frac{20}{100}$

Step 3:

By definition of percentage

$frac{20}{100}$ = 20%

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