Multiplying & Dividing Integers Section 2-7 & 2-8.
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Transcript of Multiplying & Dividing Integers Section 2-7 & 2-8.
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