Bell Ringer 58,021.349 What is the place value of the 8?

Integer Operations

The Incredible Number Line!!! The number line contains an infinite amount of points. 5, -6, 3.2, 1.115, 9.9 are all on the number line. We will deal specifically with integers, which are the whole numbers on the number line.

What is an Integer? A number with no fractional part. Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...} Examples of integers: -16, -3, 0, 1, 198 Basically integers are all positive and negative whole numbers and zero!

Adding Integers Number Line – Start at the first number and move forwards or backwards. -4 + 5 = ? Counters -4 Your answer is 1!!! 5

Huh?? Subtracting Integers Number Line – This can get confusing, but the subtraction sign changes the direction you travel in. 3 – (-4) = Counters – This isn’t much better! 3 -4 How did I get here? Huh??

Adding Integers Rules for adding integers Adding (when signs are the same) Keep the sign Add Ex. 3 + 4 = 7 Ex. (-9) + (-4) = -13 Adding (when signs are different) Keep the sign of the bigger digit Subtract Ex. -3 + 5 = 2 Ex. 4 + -7 = -3

Sample Additions -5 + 9 = -7 + -8 = 6 + (-12) = 1. The signs are different, so I find the difference, which is 4. The 9 is the bigger digit, so my answer is positive. 2. The signs are the same, so I add, which gives me 15. The signs are the same, so I keep the answer negative. 3. The signs are different, so I find the difference, which is 6. The -12 is the bigger digit, so my answer is negative.

Subtracting Integers Rules for subtracting integers ALL subtraction problems: Change the subtraction sign to an addition sign. Change the sign of the second number. Follow addition rules Ex: 3 – (- 7) = 3 + (+7) = 10

Sample Subtraction 6 – 9 = -5 – (-3) = 1. Change the subtraction to addition and change the sign of the second digit. 6 – 9 = 6 + (-9) = Follow addition rules. 6 + (-9) = -3 2. Change the subtraction to addition and change the sign of the second digit. -5 – (-3) = -5 + 3 = Follow addition rules. -5 + 3 = -2

Multiplying and Dividing Integers Rules for multiplying and dividing integers Multiply/Divide If the signs are the SAME…the answer will be POSITIVE If the signs are DIFFERENT …the answer will be NEGATIVE Ex. -4 • (-7) = 28 Ex. 5 • (-3) = -15 Ex. 25 ÷ (-5) = -5 Ex. -15 ÷ (-3) = 5

Sample Multiplying and Divding 1. The signs are different, so the answer will be negative. 5 • -8 = -40 2. The signs are the same, so the answer will be positive. -3 • -6 = -18 3. The signs are different, so the answer will be negative. -25 ÷ 5 = -5 4. The signs are the same, so the answer will be positive. -6 ÷ -2 = 3 5 • -8 = -3 • -6 = -25 ÷ 5 = -6 ÷ -2 =

Samples 1. -4 + 5 = 2. -6 – (-9) = 3. 5 • -9 = 4. -12 ÷ -3 = 1 3 -45 4