Class Notes Subtracting Integers

Class Notes Target Skill: Subtracting Integers To subtract integers, follow this rule: 1. Instead of subtracting, add the additive inverse. To do this, follow these steps: A. Change the minus sign to a plus sign. B. Change the second number to its opposite number. If it was +3, make it - 3. If it was - 62, make it + 62. C. Then, rewrite the problem. D. Now, follow the rules for adding integers. What is the additive inverse? The additive inverse is the opposite number. The opposite number is the number that you add to a number so the sum is zero. An example of opposite numbers: 6 is positive 6. The opposite of positive 6 is negative 6. +6 + (-6 ) = 0 So -6 is the opposite or additive inverse of +6. -52 is negative 52. Add positive 52 to negative 52. The answer is 0. -52 + (+52) = 0 So +52 is the opposite or additive inverse of -52. Some people call a number plus its opposite number zero pairs. You will hear that term on a lot of the videos. Zero pairs are two numbers that are opposites of each other, and that equal zero when added together.

Some subtracting integer examples: A positive number minus a positive number.

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5-3 This is the same as 5 - (+3) 1. Add the additive inverse. The additive inverse of +3 = -3 How? A. Change the minus sign to a plus sign 5 + (+3) B. Now change (+3) to its additive inverse or its opposite number. 5 + (-3). C. Now you have made what was a subtraction problem into an addition problem. D. Follow the rules for adding integers from this point on. 5 + (-3) When adding two numbers with different signs. 1. Subtract the numbers: 5 - 3 = 2 2. Keep the sign of the largest number. 5 is greater than 3. 5 is positive. Final answer = +2

Or you could do that problem the same way you have all along: 5 - 3 = 2 Another subtracting example: A negative number minus a negative number.

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-7 - (-4) 1. Add the additive inverse. The additive inverse of -4 = +4 How? A. Change the minus sign to a plus sign -7 + (-4) B. Now change (-4) to its additive inverse or its opposite number. -7 + (+4). C. Now you have made what was a subtraction problem into an addition problem. D. Follow the rules for adding integers from this point on. -7 + (+4) When adding two numbers with different signs. 1. Subtract the numbers: 7 - 4 = 3 2. Keep the sign of the largest number. 7 is greater than 4. 7 is negative. Final answer = -3

Another subtracting example. A positive number minus a negative number.

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13 - - 9 Usually written like this: 13 - (-9) 13 - (-9) 1. Add the additive inverse. The additive inverse of -9 = +9 How? A. Change the minus sign to a plus sign 13 + (-9) B. Now change (-9) to its additive inverse or its opposite number. 13 + (+9). C. Now you have made what was a subtraction problem into an addition problem. D. Follow the rules for adding integers from this point on. 13 + (+9) When adding two numbers with the same signs. 1. Add the numbers: 13 + 9 = 22 2. Keep the sign. Both numbers, 13 and 9, are positive. Final answer = + 22 On problems like this where there is this situation A number minus a negative number - (- ) I actually think of it like this A negative times a negative equals a positive.

Another subtraction example. A negative number minus a positive number.

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-7 - (+45) -7 - (+45) 1. Add the additive inverse. The additive inverse of +45 = -45 How? A. Change the minus sign to a plus sign -7 + (+45) B. Now change (+45) to its additive inverse or its opposite number. -7 + (-45). C. Now you have made what was a subtraction problem into an addition problem. D. Follow the rules for adding integers from this point on. -7 + (-45) When adding two numbers with the same signs. 1. Add the numbers: 7 + 45 = 52 2. Keep the sign. Both numbers, 7 and 45, are negative. Final answer = -52