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Exercises Numbers, fractions and percents

Example 6.41 from Prealgebra, 6.5 Solve Proportions and their Applications

Solve Proportions and their Applications: example 6.41

Determine whether each equation is a proportion:

ⓐ $\frac{4}{9} = \frac{12}{28}$
ⓑ $\frac{17.5}{37.5} = \frac{7}{15}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.

ⓐ

Find the cross products. $28 \cdot 4 = 112 9 \cdot 12 = 108$

Since the cross products are not equal, $28 \cdot 4 \neq 9 \cdot 12,$ the equation is not a proportion.

ⓑ

Find the cross products. $15 \cdot 17.5 = 262.5 37.5 \cdot 7 = 262.5$

Since the cross products are equal, $15 \cdot 17.5 = 37.5 \cdot 7,$ the equation is a proportion.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Determine whether each equation is a proportion:

ⓐ $\frac{7}{9} = \frac{54}{72}$
ⓑ $\frac{24.5}{45.5} = \frac{7}{13}$

How did it go?

PreviousSolve Proportions and their Applications: example 6.40 Next Solve Proportions and their Applications: example 6.42

From Prealgebra (1st edition) by OpenStax (Rice University), section 6.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.