Multiplying &
Dividing
Integers
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
neg x neg
or
or
pos ÷ pos
neg ÷ neg
answer is Positive!
• Opposite Signs
pos x neg
neg x pos
or
or
answer is Negative!
pos ÷ neg
neg ÷ pos
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) =
+4
( 1 )(– 4) =
+4
( 0 )(– 4) =
+4
(–1)(– 4) =
+4
(–2)(– 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) = – 72
80
– 132
125
Practice
• Example 5:
– 85 ÷ (– 5) =
• Example 6:
28 ÷ (– 4) =
2
• Example 8:
 3
45
–7
4
 –8
2
• Example 7:
3
17

–3
Evaluate the expression
When f = – 1, g = 7, and h = – 10
• Example 9:
4h
– 40
• Example 10:
• Example 11:
f hg f
gh + h
70
– 80
Evaluate the expression
When r = 12, s = – 4, and t = – 6
• Example 12:
72 ÷ t – 12
• Example 13:
ts
5
2
• Example 14:
rs ÷ 16
–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