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 25=410 512=1536 211=844

Answer 1

To determine if the fractions are equivalent, we can simplify both sides of each equation and check if they yield the same value.

1. \( \frac{13}{25} \) and \( \frac{512}{410} \)
- Simplifying \( \frac{512}{410} \):
\[
\frac{512 \div 102.4}{410 \div 102.4} = \frac{5}{4}
\]
- \( \frac{13}{25} \) is in simplest form and cannot be simplified to \( \frac{5}{4} \).
- These fractions are **not equivalent**.

2. \( \frac{512}{1536} \) and \( \frac{211}{844} \)
- Simplifying \( \frac{512}{1536} \):
- The GCD of 512 and 1536 is 512.
\[
\frac{512 \div 512}{1536 \div 512} = \frac{1}{3}
\]
- Simplifying \( \frac{211}{844} \):
- The GCD of 211 and 844 is 211.
\[
\frac{211 \div 211}{844 \div 211} = \frac{1}{4}
\]
- \( \frac{1}{3} \) and \( \frac{1}{4} \) are not equal.
- These fractions are **not equivalent**.

Therefore, based on the checks provided above, none of the presented pairs of fractions are equivalent.