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

`(14+12)* (8+12) > (14* 12)+(8* 12)`

Explanation:

First let us evaluate the value of both the expressions.

`(14+12)* (8+12) = 26* 20 = 520`

`(14* 12)+(8* 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)* (8+12) > (14* 12)+(8* 12)`

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