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.