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Converting Between Percentages and Decimals in a Real-World Situation
  • 时间:2024-10-18

Converting Between Percentages and Decimals in a Real-World Situation


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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%

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