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:

Identify the common factors of 84 and 40

Using the Factors knowledge point

$$
LATEXBLOCK0
$$

Determine the Greatest Common Factor (GCF)

Using the Greatest Common Factor knowledge point

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

Analyze Sari's applied expression

Using the Distributive Property knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given multiple-choice options

Compare the error identified with the options:

• Option 1: The listed factors of 84 are correct.
• Option 2: The listed factors of 40 are correct.
• Option 3: The expressions \(84 + 40\) and \(2(42 + 20)\) are equivalent.
• Option 4: Sari factored out 2 instead of the greatest common factor, which is 4.

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)