Question

Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same digits and the same operations.
a. Is Larry correct? Explain your thinking.
b. Which expression is greater? How much greater?

Answer 1

Answer:

$(14+12)\times (8+12) > (14\times 12)+(8\times 12)$

Step-by-step explanation:

First let us evaluate the value of both the expressions.

$(14+12)\times (8+12) = 26\times 20 = 520$

$(14\times 12)+(8\times 12) = 168 + 96 = 264$

a) Hence, Larry's claim that both the expressions are equivalent is wrong.

The evaluation of the expressions have been shown above. The second expression was obtained by swapping the addition and multiplication order and that created the difference.

b) Clearly,

520 > 264

Therefore,

$(14+12)\times (8+12) > (14\times 12)+(8\times 12)$

$(14+12)\times (8+12)$ is greater by the expression  $(14\times 12)+(8\times 12)$ by a value of 520 - 264 = 256.