Integers Rule! Dr. Deborah Santiago

What You Will Learn Some definitions related to integers. Rules for adding and subtracting integers. A method for proving that a rule is true. Are you ready??

Definition Positive number – a greater than zero

Definition Negative number – a less than zero

Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction

Definition Integers – are all the whole numbers and all of their opposites on the negative number line including zero. 7 opposite -7

Definition Absolute Value – The size of a number with or without the negative sign. The absolute value of 9 or of –9 is 9.

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level

Negative Numbers Are Used to Show Debt Let’s say your parents bought a used car, but they had to get a loan from the bank for $5,000. When counting all their money they add in a -$5,000 to show they still owe the bank.

Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 +

Solve the problems on IXL or the worksheet provided.

Integer Addition Rules Positive + = Positive: = 9 Negative + = Negative: = - 9 Sum of a negative and a positive number: Use the sign of the larger number and subtract = = = = 2

Solve the Problems = = (+3) + (+4) = = = =

Solve These Problems = = (+3) + (-4) = = = = -2 5 – 3 = – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

One Way to Add Integers Is With a Number Line When the number is positive, count to the right. When the number is negative, count to the left. +-

One Way to Add Integers Is With a Number Line =-2

One Way to Add Integers Is With a Number Line =+2

One Way to Add Integers Is With a Number Line =-4

One Way to Add Integers Is With a Number Line =+4

Solve the problems on IXL or on the worksheet provided.

Integer Subtraction Rules Keep, Change, Change, and then follow the Addition Rules! Negative - Positive = Negative: = = -8 Positive - Negative = Positive + Positive = Positive: = = 8 Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract (Change double negatives to a positive) (-5) - (-3) = ( -5) + 3 = -2 (-3) - ( -5) = (-3) + 5 = 2

Here are some more examples. 12 – (-8) 12 + (+8) = – (-11) -3 + (+11) = 8

Solve the problems on IXL or on the worksheet provided.

Integer Multiplication Rules Positive x Positive = Positive: 3 x 2 = 6 Negative x Negative = Positive: -2 x -8 = 16 Negative x Positive = Negative: -3 x 4 = -12 Positive x Negative = Negative: 3 x -4 = -12

Practice -10 x 3 = 10 x 3 = -10 x -3 = 10 x -3 =

Solve the problems on IXL or on the worksheet provided.

Integer Division Rules Positive ÷ Positive = Positive: 12 ÷ 3 = 4 Negative ÷ Negative = Positive: -12 ÷ -3 = 4 Negative ÷ Positive = Negative: -12 ÷ 3 = -4 Positive ÷ Negative = Negative: 12 ÷ -3 = -4

Practice -9 / 3 = 9 / 3 = -9 / -3 = 9 / -3 =

Solve the problems on IXL or on the worksheet provided.

Integers Rule!