1. Algebra 1
Section 1.5

2. Multiplication 3 • 5 = 5 + 5 + 5 3x means 3 • x

3. Properties of Multiplication
Commutative Property: If you multiply two numbers together in different orders, the product is the same.
ab = ba

4. Properties of Multiplication
Associative Property: If you group numbers differently when multiplying, the product is the same.
a(bc) = (ab)c

5. Properties of Multiplication
Multiplicative Identity Property: The product of any number and one is that number.
a • 1 = 1 • a = a

6. Properties of Multiplication
Distributive Property: The product of a number and a sum is equal to the sum of the products of the number and each addend.
a(b + c) = ab + ac

7. Properties of Multiplication
Zero Property of Multiplication: The product of any number and zero is zero.
a • 0 = 0

8. Multiplication A product is the answer to a multiplication problem
A factor is any number that is being multiplied in the problem

9. Multiplication Notice the pattern: 3(-5) = -15 2(-5) = -10 1(-5) = -5
0(-5) = 0
-1(-5) = 5
-2(-5) = 10
-3(-5) = 15

10. Multiplication
If the factors are both positive or both negative, the product is positive.
If one factor is positive and the other is negative, the product is negative.

11. Example 1
a. -2(9) = ____
b. -4(-6) = ____
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12. Multiplication
If there is an even number of negative factors, the product is positive.
If there is an odd number of negative factors, the product is negative.

13. Example 2
a. -2(-3)(-5) = ____
b. 4(-3)(-1) = ____
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14. Multiplication With Fractions
It is not necessary to have a common denominator.
Canceling first is usually easier.
Mixed numbers must be converted to improper fractions before multiplying.

15. Definition
A unit multiplier is a fraction with two different expressions for the same quantity in the numerator and the denominator.
Used to change the units of a number

16. Using Unit Multipliers
1 ft.
12 in.
60 in.
= 5 ft.
12 in.
1 ft.
5 ft.
= 60 in.

17. Example 6 2.54 cm a. 53.25 in. 1 in. = 135.255 cm 1 ft. b. 51 in.17
1 ft.
12 in.
= ft. 17 4
b. 51 in. 4
= 4¼ ft.

18. Example 6
5280 ft.
1 mi.
12 in.
1 ft.
c. 2 mi.
= 126,720 in.

19. Homework: pp