Question

Which pair of fractions are equivalent to 29?(1 point)
Responses

527, 1254
Start Fraction 5 over 27 End Fraction comma Start Fraction 12 over 54 End Fraction

627, 1245
Start Fraction 6 over 27 End Fraction comma Start Fraction 12 over 45 End Fraction

627, 1254
Start Fraction 6 over 27 End Fraction comma Start Fraction 12 over 54 End Fraction

2027, 1219

Answer 1

To find a pair of fractions that are equivalent to each other, you need to find two fractions that simplify to the same number or can be converted to the same fraction by multiplying or dividing both the numerator and the denominator by the same number.

Let's examine each pair:

1. \( \frac{5}{27}, \frac{12}{54} \)
These fractions are not equivalent, as \( \frac{5}{27} \) is not equal to \( \frac{12}{54} \).

2. \( \frac{6}{27}, \frac{12}{45} \)
These fractions can be simplified to see if they are equivalent:
\( \frac{6}{27} \) simplifies to \( \frac{2}{9} \) (by dividing both the numerator and the denominator by 3)
\( \frac{12}{45} \) simplifies to \( \frac{4}{15} \) (by dividing both the numerator and the denominator by 3)
These fractions are not equivalent.

3. \( \frac{6}{27}, \frac{12}{54} \)
These fractions can also be simplified:
\( \frac{6}{27} \) simplifies to \( \frac{2}{9} \) (by dividing both the numerator and the denominator by 3)
\( \frac{12}{54} \) simplifies to \( \frac{2}{9} \) (by dividing both the numerator and the denominator by 6)
These fractions are equivalent and both simplify to \( \frac{2}{9} \).

4. \( \frac{20}{27}, \frac{12}{19} \)
These fractions are not equivalent and cannot be simplified to the same value.

Thus, the pair of fractions that are equivalent and represent the same value as each other are \( \frac{6}{27} \) and \( \frac{12}{54} \).