This document discusses the rules and properties of multiplication and division. It provides examples of converting mixed numbers to improper fractions, finding products and quotients, and using order of operations. The key rules are that the product of two numbers with the same sign is positive, and the product of two numbers with different signs is negative. For division, dividing by a number is the same as multiplying by its reciprocal. Examples are provided to illustrate finding products, quotients, and solving multi-step problems using proper order of operations.

1. Ch1.5_MultiplicationAndDivision.notebook August 26, 2011
Warm up
Convert the following mixed numbers
to improper fractions
Example: 1 5 Chapter 1.5
14 4
Multiplication and Division
2
43
71
2
1
­2 5
Rules
The product or quotient of two numbers
that have the same sign is positive
Product ­ when two or more numbers are multiplied together
(+)(+) = +
Quotient ­ when a number is divided by another number
(­)(­) = +
The product or quotient of two numbers
that have different signs is negative
(+)(­) = ­
(­)(+) = ­
Rule for Division
Properties of Multiplication Dividing by a number is the same as multiplying
by the reciprocal (a.k.a. inverse)
Commutative 4 x 5 = 5 x 4
24 ÷ 6
Associative
(2 x 5) x 6 = 2 x (5 x 6)
The reciprocal of 6 is 1
6
Identity 5 x 1 = 5
1
Property of Zero 23 x 0 = 0 0 x 3425 = 0 24 x 6
Inverse
4 x (1/4) = 1 (5/16) x (16/5) = 1
(reciprocal)
1

2. Ch1.5_MultiplicationAndDivision.notebook August 26, 2011
Find the products
6 7
÷
5 9 (­2)(3.5) =
(3)(1.2)(­4) =
6 x 9
5 7 (­1)(2.3)(­2)(5) =
Example
Find the quotients
3 [ ­2.2 + 3.2 ÷ (­0.8) ]
6 7
÷
5 9
2 3
­43 ÷ 5
1.5 Worksheet
Meet in S­12 tomorrow
2