Ch. 8 Integers

1. Ch. 8 Integers

2. Understanding Rational Numbers • A rational number is any number that can be written as a quotient a/b, where a and b are integers and b is NOT equal to 0. • Examples: 3 1/8, -0.28 and 5 are all rational numbers because they can be written as 25/8, -28/100, and 5/1.

3. Graph the rational numbers on the number line. 1) -1 3/8 2) 0.75 3) -7/8 4) -1/8

4. Adding Integers • IMPORTANT THINGS TO REMEMBER: • When adding two negative numbers the answer will always be negative. Ex. -5 + -7= -12 • If you are adding a positive and a negative number. Look to see which number is larger. The larger number’s sign (+, -) will decide if the answer will be positive or negative. Ex. 5+ -7 = 7 is the bigger number so the answer will be a negative number. Ex. -6 + 11= 11 is the bigger number so the answer will be a positive number.

5. Problems • -4 + -18 = • 17 + -29= • -4 + -5 = • -8+ -5 + 6= • -18+ 18= • -20+ 4= • -3+ 2+ 2=

6. Subtracting Integers • IMPORTANT THINGS TO REMEMBER! • When subtracting two positive numbers look at the 1st number. If it is less than the second number the answer will be negative. Ex. 10-12= -2 • When you are subtracting a negative and a positive number your answer is essentially adding two negative numbers and your answer will be negative. Ex. -12-6= or -12+-6= -18

7. Subtracting continued • IMPORTANT THINGS TO REMEMBER! • When you have two negatives in a row (a subtraction sign and a negative sign) it cancels each other out and changes to a positive. Ex. 6-(-4)= There are two negatives in a row so it changes to 6+4=10 Just like English- you cannot have a double negative in a sentence! What about -2-(-7)?

8. Problems • -6-3= • -8-(-8)= • 7-12= If n=-3 evaluate each expression. 4. n-(-19)= 5. -1-n= 6. 7- l n l –(-11)=

9. Use the chart to find the difference in elevation. • Dead Sea and Mt. Everest? • Mt. Rainier and Death Valley? • Dead Sea and Death Valley? Elevation Records

10. Multiplying Integers • IMPORTANT THINGS TO REMEMBER! • The product of two positive integers is positive. Ex. 4(3)= 12 • The product of a positive and a negative integer is negative. Ex. 4(-3) or -4(3)= -12 • The product of two negative integers is positive. Ex. -4(-3)= 12

11. RULES FOR MULTIPLYING INTEGERS • The product of two integers with the same sign is always positive! • The product of two integers with different signs is always negative!

12. Problems: • 5(-6)= • (-17)2= 3. (-8)(-7)= 4. l -5 l x 6= Evaluate each expression when b=-4. • 17b • -38b • b x l -12 l x (-5)

13. Dividing Integers • Rules for Dividing Integers • The quotient of two integers with the same signs is positive. Ex. -66/-11= 6 or 54/9= 6 • The quotient of two integers with different signs is negative. Ex. -45/9= -5 or 24/ -12= -2

14. Dividing Remember the rules first and decide if the answer is going to be positive or negative. Once you have decided forget about the positive and negative signs and do normal division. REMEMBER TO ADD + or – to your answer.

15. Problems: • -32/ -8= • 0/-8= • -30 / 30= • 60/-5= • Death Valley has an elevation of -282ft. Express the Death Valley elevation in yards.