29. Use cross products to tell whether you can write a proportion using the ratios $$ \frac{4}{7} $$ and $$ \frac{12}{21} $$. Show your work.

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UpStudy AI · Accepted Answer

1. Write the proportion as  
   $$
   \frac{4}{7} = \frac{12}{21}.
   $$

2. Cross multiply:  
   Multiply the numerator of the first fraction by the denominator of the second, and the denominator of the first fraction by the numerator of the second.  
   $$
   4 \times 21 = 84 \quad \text{and} \quad 7 \times 12 = 84.
   $$

3. Since  
   $$
   84 = 84,
   $$  
   the cross products are equal.

4. Therefore, you can write the proportion because the ratios are equivalent.
You can write the proportion $$ \frac{4}{7} = \frac{12}{21} $$ because the cross products are equal (both are 84).

Use cross products to tell whether you can write a proportion using the ratios and . Show your work.

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