ratios. Are they equivalent? Explain or show $$ 3: 11 \text { and 15:55 } $$

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UpStudy AI · Accepted Answer

To determine whether the ratios $$ 3:11 $$ and $$ 15:55 $$ are equivalent, we can simplify both ratios and compare them.

### Step 1: Understand What It Means for Ratios to Be Equivalent
Two ratios $$ a:b $$ and $$ c:d $$ are **equivalent** if the fractions $$ \frac{a}{b} $$ and $$ \frac{c}{d} $$ are equal. In other words:

$$
\frac{a}{b} = \frac{c}{d}
$$

### Step 2: Simplify the Second Ratio $$ 15:55 $$

1. **Find the Greatest Common Divisor (GCD)** of the numerator and the denominator. For $$ 15 $$ and $$ 55 $$, the GCD is $$ 5 $$.
   
2. **Divide both terms of the ratio by the GCD** to simplify:
   
   $$
   \frac{15}{55} = \frac{15 \div 5}{55 \div 5} = \frac{3}{11}
   $$
   
   So, $$ 15:55 $$ simplifies to $$ 3:11 $$.

### Step 3: Compare the Simplified Ratios

Now, both ratios are:

$$
3:11 \quad \text{and} \quad 3:11
$$

Since they are identical after simplification, the ratios are **equivalent**.

### Conclusion

Yes, the ratios $$ 3:11 $$ and $$ 15:55 $$ are equivalent because both simplify to $$ 3:11 $$.
The ratios $$ 3:11 $$ and $$ 15:55 $$ are equivalent because both simplify to $$ 3:11 $$.

ratios. Are they equivalent? Explain or show \[ 3: 11 \text { and 15:55 } \]

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