Question

extend your skills

1. use cross products to tell whether you can write a proportion using the ratios \\(\frac{4}{7}\\) and \\(\frac{12}{21}\\). show your work.
2. trevor’s recipe calls for 3 cups of flour and 2 cups of sugar. he is making a larger batch and using 9 cups of flour and 4 cups of sugar.

use cross products to tell whether the ratios \\(\frac{3}{2}\\) and \\(\frac{9}{4}\\) are in proportion.
show your work.

Explanation:

Problem 29

Step1: Calculate cross products

$4 \times 21 = 84$ and $7 \times 12 = 84$

Step2: Compare cross products

Since $84 = 84$, the ratios form a proportion.

Step1: Calculate cross products

$3 \times 4 = 12$ and $2 \times 9 = 18$

Step2: Compare cross products

Since $12
eq 18$, the ratios do not form a proportion.

Answer:

Yes, the ratios $\frac{4}{7}$ and $\frac{12}{21}$ can form a proportion, as their cross products are equal (both equal to 84).

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Problem 30