Multiplication and Division of Integers

Here’s a way I can Remember! / To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use: Mr. Multiplivision

When multiplying Integers, cover the Two signs you are using Ex.: 5 (-3) What sign is left uncovered? Negative, - That is the sign of The answer = -15 Choral Response

Practice … (-10)(3) = 21  -5 = -13  -6 =

Division Good News: It’s not any different! Ex.: -48  (-4) = + 12

Reminder: Equal means it works both ways! 

Grade your boss’ work… / (4)(-7)  (-2) / First, (4)(-7) = - 28 / Finish it! (-28)  (-2) / (4)(-7)  (-2) / First, (4)(-7) = - 28 / Finish it! (-28)  (-2) Answer: 14

(-56  7)   - 7  -6 = 4 = 210 = - 135

Properties of Multiplication / Mult Identity a  1 = a and 1  a = a / Zero Property a  0 = 0 and 0  a = 0 / Property of -1 a(-1) = -a and (-1)a = - a / Mult Identity a  1 = a and 1  a = a / Zero Property a  0 = 0 and 0  a = 0 / Property of -1 a(-1) = -a and (-1)a = - a

Distributive Property / a (b+c) = ab + bc  -1 (5 + 7) = (-1)5 + (-1)7 / a (b+c) = ab + bc  -1 (5 + 7) = (-1)5 + (-1)7 How will we use this with integer multiplication? -7= (-1) 7 Also,

Here’s How to Use It Ex.: (3+-4) 6 (-1) (6) = - 6 Ex.: (3+-4) 6 (-1) (6) = - 6

Your turn / Find the answer: / 3(-2+5) = / 8(3+-6) = / Find the answer: / 3(-2+5) = / 8(3+-6) =

Multiplying Fractions

When multiplying fractions, they do NOT need to have a common denominator. To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator. If the answer can be simplified, then simplify it. Example: When multiplying fractions, they do NOT need to have a common denominator. To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator. If the answer can be simplified, then simplify it. Example: Multiplying Fractions

When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end. From the last slide: An alternative: When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end. From the last slide: An alternative: Simplifying Diagonally 1 1 You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.

To multiply mixed numbers, convert them to improper fractions first. Mixed Numbers 1 1

Multiply the following fractions and mixed numbers: Try These: Multiply

Solutions: Multiply

When dividing fractions, they do NOT need to have a common denominator. To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change. When dividing fractions, they do NOT need to have a common denominator. To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change. Dividing Fractions Change Operation. Flip 2nd Fraction.

Divide the following fractions & mixed numbers: Try These: Divide

Solutions: Divide

Homework / Page 67, #9-10 / Page 68, # 13, 15 / Page 69, #25 (do NOT do f, h, m, n, r) / Page 70, # 26, 27 / Page 72, # 44 (a-c, j-l) / Page 67, #9-10 / Page 68, # 13, 15 / Page 69, #25 (do NOT do f, h, m, n, r) / Page 70, # 26, 27 / Page 72, # 44 (a-c, j-l)