Integers

Definition Positive integer – a number greater than zero

Definition Negative number – a number less than zero

Place the following integers in order from least to greatest:

Place the following integers in order from least to greatest:

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

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

Definition Absolute Value – The distance a number is from zero on the number line The absolute value of 9 or of –9 is 9.

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Below Sea Level

Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$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 ALWAYS positive. 9 +

Integer Addition Rules Rule #1 – When adding two integers with the same sign, ADD the numbers and keep the sign = = -14

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

Check Your Answers : = = (+3) + (+4) = = = =

Solve the following: = 2. – = = 4. – =

Check Your Answers = – = = – = -49

Integer Addition Rules Rule #2 – When adding two integers with different signs, find the difference (SUBTRACT) and take the sign of the larger number = = 4 Larger absolute value: Answer = - 4

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

Solve the following: 1. – = 2. – = (-7) = 4. – =

Check Your Answers 1. – = – = (-7) = – = -55

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

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

One Way to Add Integers Is With a Number Line

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

One Way to Add Integers Is With a Number Line

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

One Way to Add Integers Is With a Number Line

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

Integer Subtraction Rule Subtracting a negative number is the same as adding a positive one. Change the sign and add. “Keep, change, change.” 2 – (-7) is the same as 2 + (+7) = 9

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

Solve the following: 1. 8 – (-12) = – (-30) = 3. – 17 – (-3) = 4. –52 – 5 =

Check Your Answers 1. 8 – (-12) = = – (-30) = = – 17 – (-3) = = –52 – 5 = (-5) = -57

Integer Multiplication Rules Rule #1 When multiplying two integers with the same sign, the product is always positive. Rule #2When multiplying two integers with different signs, the product is always negative. Rule #3If the number of negative signs is even, the product is always positive. Rule #4If the number of negative signs is odd, the product is always negative.

Solve the following: x (-12) = x +30 = 3. – 17 x (-3) = x +5 =

Check Your Answers: x (-12) = x +30 = – 17 x (-3) = x +5 = +250

Integer Division Rules Rule #1 When dividing two integers with the same sign, the quotient is always positive. Rule #2When dividing two integers with different signs, the quotient is always negative.

Solve the following: 1. (-36) ÷ 4 = ÷ -5 = 3. – 18 ÷ (-9) = ÷ +5 =

Check Your Work: 1. (-36) ÷ 4 = ÷ -5 = – 18 ÷ (-9) = ÷ +5 = +10

Evaluate the following: ² (9 – 4) = ÷ 5² + (3 - 6) =

Check Your Work: = -5 3² (9 – 4) = ÷ 5² + (3 - 7) = -6

Evaluate the following if n = -2 : (2n – 2)² n - 6

Check Your Work: (2n – 2)² n - 6

Aren’t integers interesting?