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)