Question

which one doesnt belong?
which expression does not belong and why?
a: $(2\cdot8)+(2\cdot8)$
b: $4(10 - 2)$
c: $(7 + 9)+16$
d: $12 + 20$

1. what equivalent expression would work for all 4 expressions?
2. how are the expressions similar?
3. what do you notice about the use of the parentheses?

Explanation:

Step1: Calculate value of A

$(2 \cdot 8) + (2 \cdot 8) = 16 + 16 = 32$

Step2: Calculate value of B

$4(10 - 2) = 4 \cdot 8 = 32$

Step3: Calculate value of C

$(7 + 9) + 16 = 16 + 16 = 32$

Step4: Calculate value of D

$12 + 20 = 32$

Step5: Identify non-matching structure

Expression D has no parentheses, while A, B, C use parentheses to group operations first. All expressions evaluate to 32, so D is the outlier based on structure.

Step6: Find universal equivalent expression

All expressions equal 32, so $4 \cdot 8$ or $32$ works for all.

Step7: Note similarity

All expressions simplify to the same numerical value.

Step8: Analyze parentheses use

Parentheses in A, B, C prioritize inner operations; D has no parentheses as it is a simple addition of two terms.

Answer:

1. The expression that does not belong is D. $12 + 20$: all other expressions use parentheses to group operations before completing the calculation, while this one is a direct addition of two numbers with no grouping.
2. An equivalent expression that works for all 4 expressions is $32$ (or $4 \times 8$, $16+16$, etc., any expression equal to 32).
3. All expressions are similar because they simplify to the same numerical value, 32.
4. Parentheses in expressions A, B, and C are used to group operations that need to be performed first, while expression D has no parentheses because it only involves a single addition operation with no need for prioritizing sub-operations.