Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.

Question

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

66 + 36 = 3 (22 + 12)

What statement best describes Gary’s error?
Gary did not use correct factors for 66 in the equation.
Gary did not use correct factors for 36 in the equation.
Gary did not use two equivalent expressions in the equation.
Gary did not use the greatest common factor in the equation.

Answer 1

The best statement that describes Gary’s error is:

Gary did not use two equivalent expressions in the equation.

This is because while he correctly factored out a common factor of 3, the expressions inside the parentheses (22 + 12) do not equal the original numbers (66 and 36). The correct expression using the distributive property should have used the greatest common factor (which is 6) in combination with the correct remaining expressions (which would lead to \( 6 (11 + 6) \) instead).