Question

Are 12/20 and 22/30 equivalent fractions?

A. No
B. Yes, because both fractions are divisible by 2.
C. Yes, because the difference between the denominator and numerator in each fraction is 8.
D. Yes, because they can both be simplified.

Answer 1

The fractions 12/20 and 22/30 are not equivalent because after simplification they result in 3/5 and 11/15 respectively.

The correct option is A.

Step-by-step explanation:

When examining whether 12/20 and 22/30 are equivalent fractions, we need to simplify or find a common denominator to compare them effectively. To determine if they are equivalent, both fractions can be simplified by dividing the numerator and denominator by their Greatest Common Divisor (GCD). For 12/20, the GCD is 4, so when divided, we get 3/5. Similarly, for 22/30, the GCD is 2, resulting in 11/15 after division.

To see if 3/5 and 11/15 are equivalent, we find a common denominator. Multiplying 3/5 by 3/3 gives us 9/15, which is not equal to 11/15. Hence, the original fractions, 12/20 and 22/30, are not equivalent. The correct option for the given question is A. No, as they do not simplify to the same fraction and their difference in numerators and denominators do not signify equivalence.