Download Section 3.3 – Ordering and Exponents (for Whole Numbers)

Chapter 3. Section 3
Page 1
Section 3.3 – Ordering and Exponents (for Whole Numbers)
Homework (pages 128-129) problems 1-11
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Recall that on the number line, a is less than b (a < b) if a is to the left of b on the number line
Another definition of less than for whole numbers would be that a < b if and only if there is a
nonzero whole number n such that a + n = b
NOTE: here n represents the space on the number line between a and b
Example, similar to page 128 number 1
5 < 12 because 5 + 7 = 12. Here n = 7
Example, similar to page 128 number 2
Since 2 + 8 = 10, we know that: 2 < 10, 8 < 10, 10 > 2 and 10 > 8
A compound inequality is when we combine a < x and x < b into the statement a < x < b
Properties of Inequalities:
• Transitive: If a < b and b < c, then a < c
• Additive: If a < b then a + c < b + c
• Multiplication: If a < b and c ≠ 0 , then ac < bc
What about the concept of flipping the sign when you multiply by a negative, why are we not
worrying about that here?
Exponents:
• Let a and m be any whole numbers where m ≠ 0 . Then a m = a ⋅ a ⋅ a L a (m times)
• Properties of exponents
a m a n = a m+ n
( ab) m = a mbm
( a m ) n = a mn
a m ÷ a n = a m− n
a0 = 1 ( a ≠ 0)
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Example, page 128 number 5f. Simplify 5 ⋅ 6 ⋅ 5 ⋅ 5⋅ 6⋅ 6
5 ⋅ 6 ⋅ 5 ⋅ 5 ⋅6 ⋅6 = 5 ⋅ 5 ⋅ 5 ⋅ 6 ⋅6 ⋅6 = 5 3 ⋅ 63 = (5 ⋅ 6)3
Example, page 128 number 6c. Expand (7 ⋅ 5) 3
7 ⋅7 ⋅7⋅5⋅ 5⋅ 5
Example, page 129 number 7f. Rewrite 92 ⋅123 ⋅ 2 with a single exponent
(32 ) 2 ⋅ (3 ⋅ 22 )3 ⋅ 2 = 3 4 ⋅ 33 ⋅ 26 ⋅ 2 = 37 ⋅ 27 = (3 ⋅ 2)7 = 67
Example, page 129 number 10c. Use your calculator to evaluate 3 ⋅ 54
1875
Example, page 129 number 11b. Find x where (3 x ) 4 = 320
4x = 20, so x = 5