2-3 Multiplication Of Rational Numbers

Algebra 1 2-3 Multiplying Rational Numbers

Objective 

Students will multiply real numbers

Rules for Multiplying & Dividing Integers 

The rules for multiplying real numbers are:

If the signs are the same the answer is positive  If the signs are different the answer is negative. 

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Let’s look at some examples…

Example #1 – Same Signs 

Multiply

3●3

In this instance both factors are positive The Signs are the same… so your answer will be positive 3●3= 9

Example #2 – Same Signs 

Multiply

- 3 ● (- 5)

In this instance both factors are negative Signs are the SAME… so your answer will be positive - 3 ● (- 5)

= 15

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YES…Even if both signs are NEGATIVE……

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…as long as they are the SAME…..

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…the answer will be POSITIVE when multiplying (and dividing) !! !!!

Are you sure ‘bout dat??

YES, TROG!!

Examples • 3 = 15  -6 • - 5 = 30  12 • 2 = 24  -5 • -3 = 15  -4 • 2 = -8 5

Signs are Different!!

Example #3 – Different Signs 

Multiply

5 ● (- 8)

In this instance the factors have different signs. The 5 is positive and the 8 is negative – your answer will be negative 5 ● (- 8) =

- 40

Example #4 – Different Signs 

Multiply

-6 ● 3

- 6 ● 3 = - 18

Comment 

A strategy that you can use here to make you life easy is to chunk the problem…that is

1. 2.

Multiply the numbers first… Then figure out the sign

Chunking 

Multiply

- 10 ● 4

1. Multiply 10 ● 4 first to get the total of 40 10 ● 4 = 40 2. Then evaluate for the signs – in this instance the signs are different so your answer will be negative

— ● +

=

—

The solution to the problem is: 40

-10 ● 4 = -



Remember:

Positive • Positive = Positive Negative • Negative = Positive Positive • Negative = Negative Negative • Positive = Negative

Comment  Make

no mistake about it…we will use this concept throughout this course…!!

Copy and complete these on a separate sheet for classwork. 3•4=  12(-4) =  3(2)(2) =  4² =  -2(-3)(4) = 

-3 • -6 = -2(-3) = -4(3) = -3² = -1³ =