Question

Find the sum or difference. (Lessons 1.5, 1.6)

– 41 – (– 9)

Short answer

The difference is – 32.

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.

Rule: Adding two positive integers always gives a positive integer; adding two negative integers always gives a negative integer.

Rule: 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 and then put their common sign before the answer.

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

Find the sum – 41 – (– 9) 

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

Rule: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.

Rule: Double negative is always positive. – (– 9) = + 9

Here the bigger numbers is negative and smaller number 9 is positive , subtract 9 from 41 and put the sign of the bigger number 41, the answer will be negative.

Now Evaluate:– 41+ 9 = – 32

Thus, the difference of numbers is – 32.