Integers, Absolute Value & Integer Operations

Topics Covered Absolute Value Opposites Integer Operations What are integers? Absolute Value Opposites Integer Operations Applications

What are integers? The integers are the positive and negative whole numbers together with zero. … -5 , -4 , -3 , -2, -1 , 0 , 1 , 2 , 3 , 4 , 5 , …

Absolute Value Absolute Value: Is the distance between a number and zero on the number line. Examples: |12| |-17| |53| -|47| -|-19|

Try… Find |-76| Find |84| Find -|-39|

Opposites Opposites: Are numbers which are the same distance from zero on the number line but on opposite sides of zero. Find the opposites of the following numbers 37 -42 -(63) -(-78)

Adding Integers Same Sign (moving same direction along number line) Positive + Positive = Positive Negative + Negative = Negative Opposite Signs (moving oppositive directions on number line) Subtract & take the sign of the larger number Examples: -2 + (-5) -10 + (-6) -3 + 9 12 + 3 5 + -1 (7) + (-10)

Try… (-37) + (-42) 23 + - 47 (-57) + (-213) 14 + (-15) + 20 + (-42)

Translate from words to math The sum of -23 and 49 The total of 3, -10, and 5 -5 added to the sum of -8 and 6

Application: Example #1 At midnight the temperature was -14 degrees Fahrenheit. By noon, the temperature had risen 10 degrees. What was the temperature at noon?

Application: Example #2 Ellen’s checking account balance is $23. If she writes a check For $40, what is her new balance?

Try… At 6:00AM the temperature was -4 degrees Fahrenheit. By noon, the temperature had risen by 12 degrees. What was the temperature at noon? Jorge’s checking account is overdrawn. His beginning balance was -$56. If he deposits his paycheck for $389, what is his new balance?

Subtraction Rule for Integers Change Subtraction to Addition (“Draw a Line, Change the Sign”) Change the subtraction sign to an addition sign. Change the sign of the number that follows to its opposite. Examples: 27 – (-35) -34 – (-8) 23 – 89 -17 – 43

Try… 18 - (-27) -13 – (-35) 64 – (-37) (-19) – 67

Translating Examples The difference of 70 and 98 150 decreased by 75 Subtract 10 from 16 22 less than - 90

Applications: Example #1 Temperatures on the moon range from -184 degrees Celsius during its night to 214 degrees Celsius during its day. Find the Difference between the highest and lowest temperature on the moon.

Applications: Example #2 Jeff’s balance in his checking account was $2036 at the Beginning of the week. During the week, he wrote two checks, Made two deposits, and made one ATM withdrawal. What is his ending balance? Check - $150 - $25 Paycheck $480 ATM - $200 Cash $80

Rules for Multiplying or Dividing Integers Same sign answer is positive Different signs answer is negative Would the following examples have positive or negative solutions? (- n )( m ) (-1)(-1)(-1) (-x )( -y) (-1)(0)(-1) ( a ) / ( - b ) (-10)(-10)(-10)(-10)

Try… (-6)(5) 2 • -9 -3 x -5 (24) ÷ (-6) −10 −2

Exponents An exponent represents repeated multiplication. In the expression The x is called the base and the n is called the exponent. Some examples of exponents