Tell whether the ratios form a proportion. Explain your answer.

Ask by Thornton Bush. in the United States

Jan 23,2025

Question

Tell whether the ratios form a proportion. Explain your answer. $$ \begin{array}{ll}	ext { 7. } \frac{56}{20}, \frac{24}{10} & 8 . \frac{5}{8}, \frac{42.5}{68}\end{array} $$

UpStudy AI · Accepted Answer

To determine whether the given pairs of ratios form a proportion, we need to check if the two ratios in each pair are equivalent. Two ratios $$ \frac{a}{b} $$ and $$ \frac{c}{d} $$ form a proportion if $$ a 	imes d = b 	imes c $$ or if they simplify to the same value.

Let's analyze each pair:

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### **Problem 7**

**Ratios:** $$ \frac{56}{20} $$ and $$ \frac{24}{10} $$

**Simplification:**

1. **Simplify each ratio:**
   - $$ \frac{56}{20} = \frac{56 \div 4}{20 \div 4} = \frac{14}{5} = 2.8 $$
   - $$ \frac{24}{10} = \frac{24 \div 2}{10 \div 2} = \frac{12}{5} = 2.4 $$

2. **Compare the simplified values:**
   - $$ 2.8 $$ vs. $$ 2.4 $$ → **Not equal**

3. **Alternatively, cross-multiply to verify:**
   - $$ 56 	imes 10 = 560 $$
   - $$ 20 	imes 24 = 480 $$
   - Since $$ 560 
eq 480 $$, the ratios are **not equivalent**.

**Conclusion:**  
The ratios $$ \frac{56}{20} $$ and $$ \frac{24}{10} $$ **do not form a proportion** because they are not equivalent.

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### **Problem 8**

**Ratios:** $$ \frac{5}{8} $$ and $$ \frac{42.5}{68} $$

**Simplification:**

1. **Simplify each ratio:**
   - $$ \frac{5}{8} = 0.625 $$
   - $$ \frac{42.5}{68} $$

2. **Simplify $$ \frac{42.5}{68} $$:**
   - Recognize that $$ 42.5 = 5 	imes 8.5 $$ and $$ 68 = 8 	imes 8.5 $$
   - So, $$ \frac{42.5}{68} = \frac{5 	imes 8.5}{8 	imes 8.5} = \frac{5}{8} = 0.625 $$

3. **Compare the simplified values:**
   - $$ 0.625 $$ vs. $$ 0.625 $$ → **Equal**

4. **Alternatively, cross-multiply to verify:**
   - $$ 5 	imes 68 = 340 $$
   - $$ 8 	imes 42.5 = 340 $$
   - Since $$ 340 = 340 $$, the ratios are **equivalent**.

**Conclusion:**  
The ratios $$ \frac{5}{8} $$ and $$ \frac{42.5}{68} $$ **form a proportion** because they are equivalent.

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**Summary:**

- **Problem 7:** The ratios do **not** form a proportion.
- **Problem 8:** The ratios **do** form a proportion.
Problem 7: The ratios $$ \frac{56}{20} $$ and $$ \frac{24}{10} $$ do **not** form a proportion. Problem 8: The ratios $$ \frac{5}{8} $$ and $$ \frac{42.5}{68} $$ **do** form a proportion.

Tell whether the ratios form a proportion. Explain your answer.

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