Multiplying & DividingIntegers

Section 2-7 & 2-8

Something special about ‘0’

• Zero property of multiplication–Anything times 0 = ‘zero’–‘0’ divided by anything = ‘0’

Multiplication & Division Rules!• Same Signs

pos x pos or pos ÷ pos

neg x neg or neg ÷ neg

answer is Positive!

• Opposite Signspos x neg or pos ÷ neg

neg x pos or neg ÷ pos

answer is Negative!

Why are opposites signs negative?

• Multiplication is addition repeated over and over again.

• For example, 4(– 2) is the same as:

(– 2) + (– 2) + (– 2) + (– 2) =

Why do two negatives make a positive?

• The teacher says so!

• Don’t believe? Follow the pattern:

( 2 )(– 4) =

( 1 )(– 4) =

( 0 )(– 4) =

(–1)(– 4) =

(–2)(– 4) =

+4

+4

+4

+4

What about exponents and expressions?

• Exponents: Write the equation as a product of the

same factor. Then multiply.Hint: what happens when the exponent

is even? Odd?

• Variable expressions:Substitute, and put each number in ( ).

Practice

• Example 1: – 16(– 5) =

• Example 2: 12(– 11) =

• Example 3: 5(– 5)(– 5) =

• Example 4: 4(– 3)(– 2)(– 3) =

80

– 132

125

– 72

Practice

• Example 5: – 85 ÷ (– 5) =

• Example 6: 28 ÷ (– 4) =

• Example 7:

• Example 8:

2

42

54

3 3

17

– 7

– 8

– 3

Evaluate the expression

When f = – 1, g = 7, and h = – 10

• Example 9: 4h

• Example 10:

• Example 11: gh + h

fghf

– 40

70

– 80

Evaluate the expression

When r = 12, s = – 4, and t = – 6

• Example 12: 72 ÷ t

• Example 13:

• Example 14: rs ÷ 16

5

st

– 12

2

– 3

How to keep it simple

• Again, work with just 2 numbers at a time.

• Memorize your multiplication & division rules

• Know the difference between those and the “addition” rules

• Always ask, “positive or negative?”

Homework

• Worksheet– Integers – Review rules

• Next Test!–Friday, October 3, 2008!

• Need help? Practice, practice, practice– http://www.321know.com/grade7.htm#topic186