6.5 Solve proportions and their applications (Page 4/12)

Prealgebra

Page 4 / 12

For example, $60% = \frac{60}{100}$ and we can simplify $\frac{60}{100} = \frac{3}{5} .$ Since the equation $\frac{60}{100} = \frac{3}{5}$ shows a percent equal to an equivalent ratio, we call it a percent proportion . Using the vocabulary we used earlier:

\frac{amount}{base} = \frac{percent}{100}

\frac{3}{5} = \frac{60}{100}

Percent proportion

The amount is to the base as the percent is to $100 .$

\frac{amount}{base} = \frac{percent}{100}

If we restate the problem in the words of a proportion, it may be easier to set up the proportion:

The amount is to the base as the percent is to one hundred.

We could also say:

The amount out of the base is the same as the percent out of one hundred.

First we will practice translating into a percent proportion. Later, we’ll solve the proportion.

Translate to a proportion. What number is $75%$ of $90 ?$

Solution

If you look for the word "of", it may help you identify the base.

Identify the parts of the percent proportion.
Restate as a proportion.
Set up the proportion. Let $n = number$ .	$\frac{n}{90} = \frac{75}{100}$

Identify the parts of the percent proportion.
Restate as a proportion.
Set up the proportion. Let $p = percent$ .	$\frac{9}{27} = \frac{p}{100}$

Identify the parts of the percent proportion.
Restate as a proportion.
Set up the proportion. Let $n =$ number.
Find the cross products and set them equal.
Simplify.
Divide both sides by 100.
Simplify.
Write a complete sentence that answers the question.	36 is 45% of 80.
Check if the answer is reasonable.	Yes. 45 is a little less than half of 100 and 36 is a little less than half 80.

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6.5 Solve proportions and their applications (Page 4/12)

Percent proportion

Solution

Solution

Solution

Translate and solve percent proportions

Solution

Solution

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