Nadiya determines that there are no fractions equivalent to StartFraction 2 Over 10 EndFraction with a denominator greater than 10, but less than 20, that have a whole number numerator and denominator. Is Nadiya correct?

Question

Yes, Nadiya is correct. By multiplying the numerator and denominator by 2, the first fraction equivalent to StartFraction 2 Over 10 EndFraction is StartFraction 4 Over 20 EndFraction.
Yes, Nadiya is correct. By multiplying the whole fraction by any whole number, each equivalent fraction will continue to have a denominator of 10.
No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to StartFraction 2 Over 10 EndFraction by 3 and arrive at the equivalent fraction StartFraction 3 Over 15 EndFraction.
No, Nadiya is incorrect. She could add any number between 1 and 8 to the numerator and denominator and arrive at an equivalent fraction with a denominator greater than 10 but less than 20.

Answer 1

Nadiya is incorrect in her assertion. The fraction \( \frac{2}{10} \) can be simplified to \( \frac{1}{5} \). To find equivalent fractions with a denominator greater than 10 but less than 20, you can multiply both the numerator and denominator of \( \frac{1}{5} \) by integers.

For instance:

• If we multiply by 3, we get \( \frac{3}{15} \), which has a denominator of 15.
• If we multiply by 2, we get \( \frac{2}{10} \) (which is just the original fraction).
• If we multiply by 4, we get \( \frac{4}{20} \) (which exceeds the limit of 20).

Therefore, \( \frac{3}{15} \) is an equivalent fraction with a whole number numerator and denominator between 10 and 20. Thus, the correct response would be:

No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to \( \frac{2}{10} \) by 3 and arrive at the equivalent fraction \( \frac{3}{15} \).