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Mastering Integer Multiplication and Division in a Fun Way!

Learn how to multiply and divide integers easily with the help of mnemonic "Hi I'm BOB" and practical examples. Understand the properties of multiplication, distributive property, and multiplying fractions. Practice simplifying and converting mixed numbers. Improve your skills with step-by-step guidance and homework exercises.

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Mastering Integer Multiplication and Division in a Fun Way!

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  1. Multiplication and Division of Integers

  2. Here’s a way I can Remember! • To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use: Hi I’m BOB!

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

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

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

  6. Reminder: Equal means it works both ways! 

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

  8. = 4 (-56  7)  - 2 = 210 5  -7  -6 = - 135

  9. Properties of Multiplication • Mult Identity a  1 = aand 1  a = a • Zero Property a  0 = 0and 0  a = 0 • Property of -1 a(-1) = -aand(-1)a = -a

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

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

  12. Your turn • Find the answer: • 3(-2+5) = • 8(3+-6) = 9 -24

  13. Multiplying Fractions

  14. 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: • Example:

  15. 1 1 Simplifying Diagonally • 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: You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.

  16. 1 1 Mixed Numbers • To multiply mixed numbers, convert them to improper fractions first.

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

  18. Solutions: Multiply

  19. Change Operation. Flip 2nd Fraction. Dividing Fractions • 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.

  20. Try These: Divide • Divide the following fractions & mixed numbers:

  21. Solutions: Divide

  22. 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 86, # 2-10 • Page 87, #13-18

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