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Multiplying and Dividing in Scientific Notation
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Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
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Simple Trinomials as Products of Binomials
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Multiplying and Dividing Rational Expressions
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Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 

Multiplying and Dividing Rational Numbers

After studying this lesson, you will be able to:

  • Multiply and divide rational numbers

Multiplication and Division Rule (be sure to learn this rule)

If the two rational numbers have the same sign , their product or quotient will be positive .

If the two rational numbers have different signs , their product or quotient will be negative .

For example:

Positive x Positive = Positive

Negative x Negative = Positive

Positive x Negative = Negative

 

Example 1

Since we are multiplying a negative times a positive, the answer will be negative. Remember, you dont need a common denominator when multiplying fractions. Therefore, the answer will be which reduces to .

 

Example 2 ( -3 )(4) Were multiplying a negative times a positive, therefore the answer will be -12.

 

Example 3 (-3x) ( -4y) Were multiplying a negative times a negative, therefore the answer will be 12xy. (Remember, you dont have to have like terms to multiply.)

 

Example 4

Just as with adding and subtracting, work with two numbers at a time.

Multiplying the first two fractions will give us .

Multiplying

Multiplying (the fives cancel and a positive times a positive gives us a positive )

Multiplying

 

Example 5 ÷ 36 (-4)

Since were dividing numbers with the same signs, the answer will be positive 9.

 

Example 6

Since were dividing numbers with different signs, the answer will be -12.

Example 7

Since were dividing numbers with different signs, the answer will be negative. We are dividing fractions, so we have to use the rule for dividing fractions. That rule is multiply by the reciprocal. First, we change the division sign to multiplication and we find the reciprocal of the second fraction. Now our problem looks like this: . Multiplying will give us . (note: it does not matter if the negative sign is in the numerator, the denominator, or is in front of the fraction.)

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