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

Question

15 + 21 = 3 (4 + 8)

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

Answer 1

To analyze Aida's use of the distributive property, let's first look at the expression she wrote:

15 + 21 = 3(4 + 8).

Calculating the left side, we get: 15 + 21 = 36.

Now, calculating the right side: 3(4 + 8) = 3(12) = 36.

Both sides equal 36, which means the expressions are equivalent. However, we need to determine if Aida applied the distributive property correctly and if she used the correct factor.

The common factor of 15 and 21 is actually 3, but let's break down the expressions further:

• 15 can be factored as 3 × 5.
• 21 can be factored as 3 × 7.

Thus: 15 + 21 = 3(5 + 7), not 3(4 + 8).

This means Aida's representation (4 + 8) is incorrect when decomposing the original numbers 15 and 21 since it does not correctly reflect the sum resulting from the original factors.

Therefore, the correct answer regarding Aida's error is:

B. Aida did not correctly divide by the common factor to get (4 + 8).