Question

two friends, jack and emily, are evaluating the expression (-2) × (4 + 6) using the distributive property, as shown below: jack: (-2) × 4 + (-12) emily: (-8) - (2 × 6) who evaluated the expression correctly? a both jack and emily b neither jack nor emily c emily d jack

Explanation:

Step1: Recall distributive property

The distributive property is $a\times(b+c) = a\times b + a\times c$. For $(-2)\times(4+6)$, this expands to $(-2)\times4 + (-2)\times6$.

Step2: Calculate Jack's work

Jack has $(-2)\times4 + (-12)$. Since $(-2)\times6=-12$, this matches the expanded form.

Step3: Calculate Emily's work

Emily has $(-8) - (2\times6)$. $(-2)\times4=-8$, but $(-2)\times6=-12$, which is not equal to $-(2\times6)=-12$ in this context. She misapplied the sign in the distributive step, as the expression should be $(-8) + (-12)$ not subtraction of a positive product.

Step4: Confirm correct evaluator

Only Jack correctly used the distributive property.

Answer:

D. Jack