Question

Write three different pairs of integers, each which has a sum of 24. Explain how you choose the integers.

Short answer

Three different pairs of integers, each has a sum of 24 are:

$16+8=24;48-24=24;-8+32=24$

Step-by-step solution

Apply the concept of adding or subtracting integers 

Rule: The sum of any integer and its opposite is equal to zero.

Explanation: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

Explanation: How to add or subtract the integers.

To add two numbers with the same sign, first add the two numbers ignoring the sign and then put their common sign before the answer.

To add two numbers with the opposite sign, ignore their signs and subtract the smaller number from the bigger number. Then put the sign of the bigger number before the answer.

Write three pairs of integers, each has a sum of 24. Explain. 

To add two integers, we need to check the signs of those two integers.

Rule: If they are with the same sign (positive or negative),first add the two numbers ignoring the sign and then put their common sign (positive or negative) before the answer.

Rule: If they are with the opposite sign (one is positive and other is negative), subtract the smaller number from the bigger number ignoring the sign, then put the sign of bigger number before the answer.

24 is a multiple of 8, 6 and 4, let we write each number as a multiple of 4.

First pair of integers is:$16+8=24$ (both are positive, so the answer is positive)

2^nd pair of integers is:$48-24=24$ (bigger number 48 is positive, so the answer is positive)

3^rd pair of integers is:$-8+32=24$ (bigger number 32 is positive, so the answer is positive)