INTEGERS SOL 7.5 Benchmarks 7.6 You have worked with positive numbers in the past - numbers greater than zero. We are now going to work with negative numbers - numbers less than zero. Think of some "real-life" examples of negative numbers. Please describe three examples of where you have seen negative numbers in the real world.

Number Line Line Jumper Virtual Math The number line is a line labeled with the integers in increasing order from left to right, that extends in both directions: For any two different places on the number line, the integer on the right is greater than the integer on the left. Example: 9 > 4, 6 > -9, -2 > -8, and 0 > -5

Absolute Value Absolute Value is defined as the distance a number is from zero on the number line. The symbol for absolute value is two straight lines on either side of the number : l 6 l = 6 Absolute value is always positive, because it is a distance.

Adding Integers Chapter 2 Section 3 When adding integers of the same sign, we add their absolute values, and give the result the same sign. Examples: = 7 (-7) + (-2) = -9 (-80) + (-34) = -114

Adding numbers with the same sign! If the signs are the same add the numbers and keep the signs. EX : 5+37EX : (-62) + (-13) 42-75

Additive Inverse Any two numbers whose sum is zero. Note that 53 and -53 are opposite integers. All opposite integers have this property that their sum is equal to zero. Two integers that add up to zero are also called additive inverses (-53) = ? {side note} What is a sum??? It’s the answer to an addition problem

The additive inverse! Of 4 is…Of 9 is…Of -61 is… Of -.367…Of 9/3 is…Of is….367-9/34593

Adding with different signs… Ex : 6+(-4)Ex : = Negative numbers = Positive numbers 2 4 When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value.

More adding integers with different signs Example: 8 + (-3) = ? The absolute values of 8 and -3 are 8 and 3. Subtracting the smaller from the larger gives = 5, and since the larger absolute value was 8, we give the result the same sign as 8, so 8 + (-3) = 5. Example: 8 + (-17) = ? The absolute values of 8 and -17 are 8 and 17. Subtracting the smaller from the larger gives = 9, and since the larger absolute value was 17, we give the result the same sign as -17, so 8 + (-17) = -9. Example: = ? The absolute values of -22 and 11 are 22 and 11. Subtracting the smaller from the larger gives = 11, and since the larger absolute value was 22, we give the result the same sign as -22, so = -11.

Subtracting Subtracting an integer is the same as adding its opposite. EX: 10 – (-2) 8 EX: 32- (-4) 32 + (+4) 36 Examples: In the following examples, we convert the subtracted integer to its opposite, and add the two integers = 7 + (-4) = (-5) = 12 + (5) = = -8 + (-7) = (-40) = (40) = 18 Note that the result of subtracting two integers could be positive or negative.

Try these! Line Jumper SUBTRACTING INTEGERS

Multiplication & Division If multiplying or dividing a pair of integers with the same sign, the answer will be positive. EX: 4 × 3 = 12 EX: (-4) × (-5) = 20 EX: (-24) ÷ (-3) = 8 EX: (-98) ÷ (-7) = 14 If multiplying or dividing a pair of integers with different signs, the answer will be negative. EX: (-7) × 6 = -42 EX: 12 × (-2) = -24 EX: (-100) ÷ 25 = -4 EX: 98 ÷ (-7) = -14

More Application Problems… (click here)Application Problems… Problem: George owes his friend Jeanne $3. If he borrows another $6, how much will he owe her altogether? Solution: This problem is quite simple: just add $3 and $6 and the result is $9. Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations? Click here for more like this…Click here for more like this…

VOCABULARY Integer Expression Rule Solve Number Line Absolute Value Negative Number Positive number Opposite Additive Inverse Zero Pair

Connected Math Accentuate the Negative

United Streaming The Power of Algebra: Positive and Negative Numbers The Zany World of Math: Adding, Subtracting, Multiplying & Dividing Integers Click here for more activities…