1. IntegersIntegers Add, subtract, multiply, and divide.

2. Positive and negative numbers can represent or describe many different situations.

3. Using integers to represent quantities. Numbers on a number line. Temperatures on a thermometer: Temperature above zero degrees are positive (+10°) and temperatures below zero degrees are negative (-10°). Altitude: An airplane leaves the airport and climbs to an altitude (height) of 2500 feet (+2500). To land, the plane must lose 2500 feet of altitude (-2500)

4. Sports scores: If your favorite football team gained 4 yards during the game, it could be represented by +4. Should your team lose 4 yards, it could be represented by -4. Profit and loss: A candy store lost $28,400 (-28,400) the first year of business but recovered the amount (+28,400) the second year. Recorded time: When referring to historical times, 2000 years BC (-2000) can be compared to 2000 years AD (+2000). Elevator movement: The elevator went up 15 floors (+15), and then went down 10 floors (-10).

5. Integer – the set of all whole numbers and their opposites. Opposite – two numbers that are equal distance from zero on a number line (-5 and 5); also called additive inverse. Absolute value – the distance a number is from zero, it is a measure of distance so the number is always positive. (symbol) |-5|

6. Number Groups

7. Natural number or counting numbers… 1, 2, 3, 4, 5, 6, 7, 8, 9 Whole number… All the counting numbers plus 0 Integer… The set of all whole numbers and their opposites; 5, 4, 3, 2, 1, 0, -1, -2, -3, -4 Rational number… Any number that can be expressed as a fraction; 6/1, and 0.5 as ½, these numbers will be either repeating or terminating decimals. Irrational number… A number that cannot be expressed as a fraction; √3 = 1.732050808…

8. Absolute Value

9. IntegersIntegers Only four operations Add, subtract, multiply and divide

10. Adding Integers Rules: When you add 2 numbers with the same sign, 1)Add the absolute values, and 2)Write the sum (answer) with the sign of the numbers. When you add 2 numbers with different signs, 1)Subtract the absolute values, and 2)Write the difference (answer) with the sign of the number having the larger absolute value.

11. Complete the following problems

12. Remember: When the signs are the same, add and keep the sign. When the signs are different, subtract and take the sign of the larger number. 1)-9 + (-7) = 2)-20 + 15 = 3)(-23) + (-7) = 4)3 + 5 = 5)6 + (-2) = 6)(-21) + 21 = 7)-3 + 8 = 8)-9 + 6 = 9)-9 + (-5) = 10)(-7) + 3 + (-12) =

13. Subtracting integers Rule: You can subtract integers by adding is opposite.

14. Remember: add its opposite 1)9 – (-3) = 9 + (+3) = 2)-7 – (-5) = -7 + (+5) = 3)21 – (-19) = 21 + (+19) = 4)-5 – 4 = -5 + (-4) = 5)-10 – (-15) = -10 + (+15) = 6)-25 – (+25) = -25 + (-25) = 7)3 – (+5) = 3 + (-5) = 8)9 – 3 = 9 + (-3) = 9)10 – (-5) = 10 + (+5) = 10)-14 – 4 = -14 + (-4) =

15. Multiplying and Dividing Integers Rules: Multiplying… The product of 2 numbers with the same signs is positive. The product of 2 numbers with different signs is negative. Dividing… The quotient of 2 numbers with the same signs is positive. The quotient of 2 numbers with different signs is negative.

16. Multiplying and Dividing integers

17. Remember: Same signs = positive (+) product or quotient. Different signs = negative (-) product or quotient. 1)3 · (-5) = 2)(-8) · 7 = 3)(-6) · (-5) = 4)(4)(3) = 5)-12 ÷ (-3) = 6) -27 ÷ 3 = 7)-6 ÷ (-8) = 8)-18/2 = 9)(-5) · (-3) = 10)-24/6 =

18. Real-World Problem Solving John’s bank account was overdrawn. The balance of his account was -$4.15. He did not realize he was overdrawn and wrote another check for $25.00. The bank charged him a $20.00 fee for being overdrawn. What was the new balance of John’s account? During one week of testing at the nuclear power plant, electrical output dropped 534 kilowatts. During the next 4 weeks, output increased 356 kilowatts, decreased 650 kilowatts, increased 334 kilowatts and increased 351 kilowatts. What was the net change (increase or decrease) in kilowatt output during the testing?

19. Solving Equations with Integers When solving equations with integers, your goal is the same as with whole numbers; isolate the variable on one side of the equation. Y + 8 = 6 Subtract 8 from both sides. Y + 8 – 8 = 6 – 8 Y + 0 = -2 Identity property of Zero, y + 0 = y Y = -2 Check: Y + 8 = 6 (-2) + 8 = 6? true

20. Solve. 1)T – 9 = -22 2)Y + 6 = -31 3)34 = -2m 4)c/-7 = -12 5)S + 3 = -8 6)Z – 12 = 4 7)16 = -4h 8)x/-3 = -8 9)9 = 2x + 1 10) 2a – 7 = -9