Lesson 11Lesson 11

Addition, Subtraction, Addition, Subtraction, Multiplication, and Division of Multiplication, and Division of

IntegersIntegers

Rules for Adding IntegersRules for Adding Integers

When the signs are the same, keep the When the signs are the same, keep the sign and add.sign and add.

When the signs are different, take the sign When the signs are different, take the sign of the number with the higher absolute of the number with the higher absolute value and subtract.value and subtract.

Example 1Example 1

6 + (-14) + (-10) + 30 =6 + (-14) + (-10) + 30 = Strategy: Follow the rules for adding Strategy: Follow the rules for adding

integers.integers. Step 1: Add the positive integers.Step 1: Add the positive integers. 6 + 30 = 366 + 30 = 36 Step 2: Add the negative integers.Step 2: Add the negative integers. (-14) + (-10) = (-24)(-14) + (-10) = (-24)

Step 3: Add the solutions from Steps 1 Step 3: Add the solutions from Steps 1 and 2.and 2.

36 + (-24) = 1236 + (-24) = 12

SolutionSolution

The answer is 12.The answer is 12.

Rules for Subtracting IntegersRules for Subtracting Integers

Rewrite the subtraction problem as an Rewrite the subtraction problem as an addition problem:addition problem:

Change the minus to a plus.Change the minus to a plus. Change the sign of the number to be Change the sign of the number to be

subtracted (the second number). If the subtracted (the second number). If the second number is positive, make it second number is positive, make it negative; if the second number is negative; if the second number is negative, make it positive.negative, make it positive.

Solve using the rules for addition.Solve using the rules for addition.

Example 2Example 2

Subtract: 16 – (-13) =Subtract: 16 – (-13) = Strategy: Rewrite the problem as an Strategy: Rewrite the problem as an

addition problem.addition problem. Step 1: Rewrite the problem.Step 1: Rewrite the problem. 16 + 13 =16 + 13 = Step 2: Add.Step 2: Add. 16 + 13 = 2916 + 13 = 29

SolutionSolution

The answer is 29.The answer is 29.

Rules for Multiplying IntegersRules for Multiplying Integers

If the signs are alike, the answer is If the signs are alike, the answer is positive.positive.

If the signs are different, the answer is If the signs are different, the answer is negative.negative.

Example 3Example 3 (-25) x (-8) x (-2) =(-25) x (-8) x (-2) = Strategy: Follow the rules for multiplying Strategy: Follow the rules for multiplying

integers.integers. Step 1: Multiply the numbers.Step 1: Multiply the numbers. 25 x 8 x 2 = 40025 x 8 x 2 = 400 Step 2: Determine the sign of the answer.Step 2: Determine the sign of the answer. (-) x (-) = (+); (+) x (-) = (-)(-) x (-) = (+); (+) x (-) = (-) The sign of the answer is negative.The sign of the answer is negative. -400-400

SolutionSolution

The product is -400.The product is -400.

Rules for Dividing IntegersRules for Dividing Integers

If the signs are alike, the answer is If the signs are alike, the answer is positive.positive.

If the signs are different, the answer is If the signs are different, the answer is negative.negative.

Example 4Example 4

Divide: (-20) / (5) =Divide: (-20) / (5) = Strategy: Follow the rules for dividing Strategy: Follow the rules for dividing

integers.integers. Step 1: Divide the numbers.Step 1: Divide the numbers. 20 / 5 = 420 / 5 = 4 Step 2: Determine the sign of the answer.Step 2: Determine the sign of the answer. The signs are different; negative.The signs are different; negative. -4-4

SolutionSolution

The quotient is -4.The quotient is -4.