Final answer:
Nadiya is correct that there are no equivalent fractions to 2/20 with denominators between 10 and 20 that give a whole number numerator, as these would not be simplifications but rather the same fraction or fractions with a non-whole numerator.
Step-by-step explanation:
Nadiya is incorrect in her determination that there are no fractions equivalent to 2/20 with a denominator greater than 10 but less than 20 that give a whole number numerator. To find equivalent fractions, one must find a number that both the numerator and the denominator can be multiplied by to yield a new fraction with the same value. The fraction 2/20 can be simplified to 1/10 by dividing both numerator and denominator by 2. From there, we can look for denominators greater than 10 but less than 20 to create equivalent fractions. A denominator of 12 cannot be used since 10 does not multiply into 12 evenly. However, if we take a denominator like 15, we find that 10 multiplies into 15 with a factor of 1.5. Therefore, multiplying both numerator and denominator of 1/10 by 1.5 gives us the equivalent fraction 1.5/15, which does NOT have a whole number numerator. If we try a denominator of 20, then multiplying 1/10 by 2 gives us the equivalent fraction 2/20, which we started with. Hence, Nadiya’s determination is correct that there are no fractions with a denominator between 10 and 20 that give a whole number numerator when looking for equivalents to 2/20.