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Multiplication and Division of Real Numbers - Section 1.7
Recall that the numbers that are multiplied are called factors and the result is called the product. In the example
below, 3 and 5 are the factors.
3
5
3 5
35
3 5
3 5
15
product
Product of Two or More Numbers
1. If no factor is zero, multiply the absolute value of all factors. The sign of the product is positive if there are an
even number of negative numbers and negative if there are an odd number of negative numbers.
2. If any factor is 0, the product is 0.
Examples: Multiply.
2
3
5
7
3 1 4
12
2
3
2
12. 3 245 0 11. 4
Division of Real Numbers
The result of dividing a real number a by a real number b is called the quotient.
Two numbers whose product is 1 are called multiplicative inverses or reciprocals of each other. For example,
the multiplicative inverse of 3 is 13 since 3 13
1
Find the multiplicative inverse in each case:
1
5
3
7
6
If a and b are non-zero real numbers, then the quotient of a and b (or a divided by b is defined as
a
b
a
1
b
a
b
Because the quotient is defined as a product, the sign rules for dividing are the same as for multiplying.
1
Division Involving Zero
1. Division of any number by zero is undefined.
2. Any nonzero number divided into zero is 0.
Examples: Divide.
27
15
3
9
4
5
2
15
12. 48
0. 2
0
13
12
0
Identity Property of Multiplication: a 1
Inverse Property of Multiplication: a
Multiplication Property of 1 : 1 a
a
1
a
1
a or a 1
a
a
Important note: If a negative sign precedes parentheses or any grouping symbol, use the distributive property to
change the sign of all terms inside the grouping symbol. For example:
x
2y
7
1 x
1
2y
1 7
x
2y
7
Simplify the following algebraic expressions:
1.
3 4x
2. 7b
9b
2
3.
2x
4. 5 x
6y
y
2x
3y
Determine whether 3 is a solution to the equation 2x
5
6x
7
Application:
Based upon data from the U.S. Department of Education, the percentage of bachelor’s degrees earned by women,
W, and the percentage of bachelor’s degrees earned by men, M, can be described by the following mathematical
models:
W
0. 28n
53
and
M
0. 28n
47
where n is the number of years after 1989.
According to these models, what is the estimated percentage of bachelor’s degrees earned by women and men in
2009?
Write a formula that models the ratio, R, of the percentage of bachelor’s degrees earned by women to the
percentage of bachelor’s degrees earned by men. Use this model to find this ratio in 2014
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