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 saris 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.

Explanation:

Find the common factors

Using the Factors knowledge point

$$
LATEXBLOCK0
$$

Determine the greatest common factor

Using the Greatest Common Factor knowledge point

$$ \text{GCF}(84, 40) = 4 $$

Analyze Sari's expression

Using the Distributive Property knowledge point

$$
LATEXBLOCK1
$$

Identify the error statement

The statement that best describes Sari's error is:
"Sari did not use the greatest common factor in the equation."

Answer:

• 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. (Correct answer)