1-6 to 1-8 Integers What You’ll Learn To find opposite and absolute value To order integers To add integers To subtract integers and find range To multiply integers To divide integers

Understanding Integers Integers are the set of positive and negative whole numbers, including zero. Numbers to the right of 0 on a number line are positive and numbers to the left of 0 are negative. The number -3 is a negative integer and the number 3 is a positive integer. The number zero is neither positive nor negative, it is neutral. Each point is and integer

Finding the Opposite Find the opposite of -4 Find the Opposite of: The opposite of -4 is + 4 because the two integers are each 4 units from zero on the number line Find the Opposite of: -8 13 -22

Finding Absolute Value The absolute value of a number is its distance from 0 on a number line You write “the absolute value of -3 as /-3/ Therefore 3 and /-3/ are the same because they are the same distance from zero

Comparing Integers You can compare and order integers by graphing. Numbers increase in value from left to right Compare -7 and 1 using the symbols below

-5 is 5 units to the left of 0 1 is 1 unit to the right of 0 Numbers increase from values from left to right Therefore -5 < 1

Practice Compare using symbols -8__ 2 2___-2 3___-3 Order the numbers from least to greatest 3,-1,-4, and 2 Practice: Text page 36 #1-39 3’s Assign Pr, Re, & En 1-6

Adding Integers When adding two integers with the same sign, add their absolute values. Then give the sum (answer) the sign of the integers. -3 + -2 = ? |-3| + |-2| = ? 3 +2 = 5, then make the result negative.

Adding Integers When adding integers with different signs, first find their absolute values. Then subtract the lesser absolute value from the greater absolute value, and give the result the sign of the integer with the greater absolute value. -7 + 3 = ? |-7| = 7 and |3| = 3 (find the absolute values) 7 - 3 = ? (subtract the lesser from the greater) 7 - 3 = 4 /-7/ > /3/ (keep the sign of the greater absolute value) - 4

Now You Try!!! 1. 65 + -7 = A. -72 B. 72 C. 58 D. -58 2. -98 + -21 = 1. 65 + -7 = A. -72 B. 72 C. 58 D. -58 2. -98 + -21 = A. 77 B. -119 C. -77 D. 119 3. -8 + 9 = A. -17 B. -1 C. 1 D. 17 Practice: Text page 42 # 1-25

Subtracting Integers Subtracting integers is the same as adding the opposite. 3 - -7 = ? 3 + +7 = 10 (add the opposite) 3 + 7 = 10

Example 1: 25 - -10 = ? Solution: Subtracting a negative number creates a positive, so the problem can be rewritten as: 25 + 10 = ? 25 + 10 = 35

Example 2: -48 - -18 = ? Step 1: Rewrite the problem as: -48 + 18 = Step 2: Remember the rules for adding integers: To add two integers with different signs, first find their absolute values. Then subtract the lesser absolute value from the greater absolute value. Give the result the sign of the integer with the greater absolute value. So we first find the absolute values. |-48| = 48 |18| = 18 Step 3: Subtract the lesser absolute value from the greater value. 48 - 18 = 30 Step 4: Give the result the sign of the integer with the greater absolute value. Since 48 is the greater absolute value, we give the result a negative sign. -48 + 18 = -30 Practice: Text page 42 # 26-38; 44-52

Range The range of a data set is the difference between the greatest and the least values

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Finding the Range The range of a data set is the difference between the greatest and the least values Temperatures a Verkhoyansk, Russia, have ranged from a low of -90 F to a high of 98 F. Find the temperature range in Verkhoyansk 98 – (-90) = 98 + 90 << Add the opposite of -90 = 188 Find each range 53 to -47 -42 to -8 Assign: Pr, Re, & En 1-7

Find the range… Between 24 and – 2 Between 7 and -3 Between 6 and – 6

Multiplying Integers To multiply integers, follow these rules. •The product of two positive integers is positive (Example: 9 x 4 = 36). •The product of a positive integer and a negative integer is negative (Example: 9 x -4 = -36). •The product of two negative integers is positive (Example: -9 x -4 = 36). Notice from the above examples that when you multiply integers with the same sign, the answer is positive. When multiplying integers with different signs, the answer is negative

Multiply these Integers 5 (3) = 5 (-3) = - 5 (3) = -5 ( - 3) =

Dividing Integers To find the quotient (answer to a division problem) of two integers, the following rules apply: The quotient of two integers with different signs is negative. Example: 16 ÷ -4 = -4. The quotient of two integers with the same sign is positive. Examples: 16 ÷ 4 = 4 and -16 ÷ -4 = 4 Practice: Text page 47 #1-24 Assign Pr & Re 1-8

Divide these Integers 14 / - 2 = - 32 / -8 = -56 / - 7 = -121 / 11 =