Multiplication and Division

of Integers

Multiplication and Division

of Integers

Here’s a way I can Remember!

Here’s a way I can Remember!

To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use:

To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use:

Mr. Multiplivision

When multiplyingIntegers, 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:Reminder:

Equal means it works both ways!

Equal means it works both ways!

Grade your boss’ work…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) - 2

5 -7 -6

= 4

= 210

= - 135

Properties of MultiplicationProperties 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 PropertyDistributive 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) 7Also,

Here’s How to Use ItHere’s How to Use It

Ex.: (3+-4) 6

(-1) (6) = - 6

Ex.: (3+-4) 6

(-1) (6) = - 6

Your turnYour turn

Find the answer:

3(-2+5) =

8(3+-6) =

Find the answer:

3(-2+5) =

8(3+-6) =

9 9

-24 -24

Multiplying FractionsMultiplying 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:

• 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:

Multiplying FractionsMultiplying FractionsMultiplying FractionsMultiplying 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 DiagonallySimplifying DiagonallySimplifying DiagonallySimplifying 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.

• To multiply mixed numbers, convert them to improper fractions first.

Mixed NumbersMixed NumbersMixed NumbersMixed Numbers

1

1

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

Try These: MultiplyTry These: MultiplyTry These: MultiplyTry These: Multiply

Solutions: MultiplySolutions: MultiplySolutions: MultiplySolutions: 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 FractionsDividing FractionsDividing FractionsDividing Fractions

Change Operation.

Flip 2nd Fraction.

• Divide the following fractions & mixed numbers:• Divide the following fractions & mixed numbers:

Try These: DivideTry These: DivideTry These: DivideTry These: Divide

Solutions: DivideSolutions: DivideSolutions: DivideSolutions: Divide

HomeworkHomework

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)