Aida applied the distributive property to write the equivalent expressions below.

Question

15 + 21 = 3 (4 + 8)

What is Aida’s error?
Aida used 3 as the factor, which is not common to 15 and 21.
Aida did not correctly divide by the common factor to get (4 + 8).
Aida did not apply the correct operations to the expressions.
Aida wrote two expressions that are not equivalent.

Answer 1

Aida's error is: Aida used 3 as the factor, which is not common to 15 and 21.

To break it down:

• The numbers 15 and 21 can be factored by their greatest common factor, which is 3. So, both numbers can indeed be divided by 3.
• However, if you take 15 and 21 and factor them as 3(5) and 3(7) respectively, it does not lead to the addition of (4 + 8) since 5 + 7 equals 12, not 12.

Essentially, her original equation does not hold true as 15 + 21 = 36, while the right side 3(4 + 8) equals 3(12) = 36, but the way she's broken it down does not justify her expression. Thus, the first option correctly identifies the issue with the factor used.