Question

Are the fractions equivalent? If so,what number were both the numerator and denominator multiplied by to arrive at the equivalent fraction?(4 points) 13=512 %C2%A0 25=410 %C2%A0 512=1536 %C2%A0 211=844

Answer 1

To determine if the pairs of fractions are equivalent, we can simplify them or cross-multiply.

1. **For the first pair:** \( \frac{13}{25} \) and \( \frac{512}{410} \).

- Cross multiplying:
\[
13 \times 410 = 5330
\]
\[
25 \times 512 = 12800
\]
- Since \( 5330 \neq 12800 \), these fractions are **not equivalent**.

2. **For the second pair:** \( \frac{512}{1536} \) and \( \frac{211}{844} \).

- Simplifying \( \frac{512}{1536} \):
\[
512 \div 512 = 1 \quad \text{and} \quad 1536 \div 512 = 3 \quad \Rightarrow \quad \frac{512}{1536} = \frac{1}{3}
\]
- Simplifying \( \frac{211}{844} \):
\[
211 \div 211 = 1 \quad \text{and} \quad 844 \div 211 = 4 \quad \Rightarrow \quad \frac{211}{844} = \frac{1}{4}
\]
- Since \( \frac{1}{3} \neq \frac{1}{4} \), these fractions are **not equivalent**.

3. **Conclusion:** Both pairs of fractions are not equivalent.