Question

Compare 10+(-2) and -10+2. Can you use this to find the sum [10+(-2)] + (-10+ 2) without performing any additions?

a) 10+(-2) is equal to -10+2.
b) You cannot find the sum without performing additions.
c) The sum of [10+(-2)] + (-10+ 2) is 0.
d) [10+(-2)] + (-10+ 2) equals 20.

Answer 1

The correct answer is C.

10 and -10 are additive inverses, as are 2 and -2.

Answer 2

The sum of [10+(-2)] + (-10+ 2) is 0 because each expression is the additive inverse of the other, hence they cancel each other out.

Step-by-step explanation:

When comparing 10+(-2) and -10+2, it is evident that the expressions are not equal. The expression 10+(-2) equals 8, because when a positive number and negative number are added, the smaller number is subtracted from the larger one, with the result taking the sign of the larger number. Conversely, -10+2 results in -8, following the same rule but with -10 being the larger number in absolute value.

To find the sum of [10+(-2)] + (-10+ 2) without performing any additions directly, we can recognize that each expression is the additive inverse of the other. Therefore, their sum is zero because additive inverses cancel each other out. This confirms that the correct answer is c) The sum of [10+(-2)] + (-10+ 2) is 0.