Lesson 1: Operations with Integers

Standards: none. Prerequisite

• Adding Integers with the same sign (both positive or both negative):

Example 1: 5 + 7

Model:

Example 2:-5 + (-7)

Model:

• Adding Integers with different signs (one positive number and one negative number)

Example 3: -5 + 7

Model:

Example 4:5 + (-7)

Model:

Summary of Addition:

Addition Examples

• -6 + 4 =• 4 + (-6) = • -3 + (-8) =• 9 + (-3) =• -7 + (-4) = • -8 + (-13) =• 5 + (-3) =

Addition Examples 2

• A scuba diver who is 88 ft below sea level begins to ascend to the surface. What is his new depth after rising 37 feet?

• The temperature one winter morning is -14⁰F. What is the new temperature after a decrease of 11 degrees?

Subtraction is really addition in disguise.

Two minus signs in the middle become a plus:Example: Change to: Answer:

12 – (-7) 12 + 7 19

-15 – (-3)

8 – (-4)

One minus sign in the middle just means the 2nd number is negative. Use the rules of addition. Don’t say “minus” say “and negative”.Example: Say: Answer:

- 9 – 4 = Negative 9 and negative 4 or -9 + (-4)

-13

7 – 10 =

- 5 – 10 =

Multiplying and Dividing numbers that have the same sign (both positive or both negative). Multiply or Divide as usual and your

answer will be a positive number.

Multiplying Dividing

6(8) = 24 / 3 =

-11(-9) = -20/-4 =

Multiplying and Dividing numbers that have different signs (one is positive and one is negative). Multiple or Divide as usual and your answer will be a negative number.

Multiplying Dividing

-4(9) = -49/7=

8(-7) = 64/-4=

Exponents

Examples: 2)4(

33

42

2)6(

28

2)7(

Evaluating an ExpressionAn expression is a mathematical phrase that can contain numbers, variables, and

operating symbols (such as +, -, *, or /). We “evaluate” an expression when we replace the variables with the numbers they represent, and do the arithmetic.

• Evaluate the expression xy + z if x = -4, y = 3, and z = -3.

• Evaluate the expression if d = -6 and e = -3.

• We will do more evaluating in later lessons.

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More examples

• Simplify: (-3)(-3)(2)(2)(-1) =• A Mach number M indicates the speed of a supersonic airplane. You can

find the airplanes’ speed, a, in miles per hour using the formula a = Ms where s is the speed of sound at the altitude of the airplane. Find an airplane’s speed in miles per hour if the airplane travels at Mach 2.5 at an altitude where the speed of sound is 710 mi/h.

• Use the table below. What is the average temperature for the week?

Day Mon Tues Wed Thurs Fri Sat Sun

Temp -3 4 -2 -5 -3 1 1