Question

Sari applied the distributive property using the greatest common factor to determine the expression that is equivalent to 84 +40. Her work is shown below.

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

84 + 40 = 2 (42 + 20)

What statement best describes Sari’s error?
Sari did not use correct factors for 84 in the equation.
Sari did not use correct factors for 40 in the equation.
Sari did not use two equivalent expressions in the equation.
Sari did not use the greatest common factor in the equation.

Answer 1

The correct statement that best describes Sari’s error is:

**Sari did not use two equivalent expressions in the equation.**

Explanation: When applying the distributive property using the greatest common factor, you need to factor both numbers correctly in such a way that the expression can be rewritten as a product of that factor and the sum of the equivalent expressions. In Sari's case, while she correctly identified that both 84 and 40 can be divided by 2, she did not correctly rewrite the sum as a combination of the sums of their respective factors (i.e., 84 + 40 should be expressed as 2(42 + 20), where both 42 and 20 appropriately represent the original numbers when factored out). Thus, while 2 is a common factor, the way she combined the expressions did not maintain their equivalency to the original addition.