Translating Phrases to Expressions with Fractions

Have you noticed that the examples in this section used the comparison words ratio of, to, per, in, for, on, and from? When you translate phrases that include these words, you should think either ratio or rate. If the units measure the same quantity (length, time, etc.), you have a ratio. If the units are different, you have a rate. In both cases, you write a fraction.

Example

Translate the word phrase into an algebraic expression:

$\phantom{\rule{0.2em}{0ex}}427$ miles per $h$ hours

$\phantom{\rule{0.2em}{0ex}}x$ students to $3$ teachers

$\phantom{\rule{0.2em}{0ex}}y$ dollars for $18$ hours

Solution


	$\text{427 miles per}\phantom{\rule{0.2em}{0ex}}h\phantom{\rule{0.2em}{0ex}}\text{hours}$
Write as a rate.	$\frac{\text{427 miles}}{h\phantom{\rule{0.2em}{0ex}}\text{hours}}$


	$x\phantom{\rule{0.2em}{0ex}}\text{students to 3 teachers}$
Write as a rate.	$\frac{x\phantom{\rule{0.2em}{0ex}}\text{students}}{\text{3 teachers}}$


	$y\phantom{\rule{0.2em}{0ex}}\text{dollars for 18 hours}$
Write as a rate.	$\frac{\$y}{\text{18 hours}}$

This lesson is part of:

Introducing Decimals

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	\(\text{427 miles per}\phantom{\rule{0.2em}{0ex}}h\phantom{\rule{0.2em}{0ex}}\text{hours}\)
Write as a rate.	\(\frac{\text{427 miles}}{h\phantom{\rule{0.2em}{0ex}}\text{hours}}\)


	\(x\phantom{\rule{0.2em}{0ex}}\text{students to 3 teachers}\)
Write as a rate.	\(\frac{x\phantom{\rule{0.2em}{0ex}}\text{students}}{\text{3 teachers}}\)


	\(y\phantom{\rule{0.2em}{0ex}}\text{dollars for 18 hours}\)
Write as a rate.	\(\frac{\$y}{\text{18 hours}}\)