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Thursday 21st of November



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	Factoring Trinomials with Leading Coefficient 1
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	Simplifying Expressions with Negative Exponents
	Solving Equations 3
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	Power of a Quotient Property of Exponents
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	The Quadratic Formula
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	Polar Form of a Complex Number
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	Simplifying Complex Fractions
	Algebra
	Common Logs
	Operations on Signed Numbers
	Multiplying Fractions in General
	Dividing Polynomials
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	Higher Degrees and Variable Exponents
	Solving Quadratic Inequalities with a Sign Graph
	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
	Solving Linear Equations
	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
	fractions
	Rotating an Ellipse
	Multiplying Numbers
	Linear Equations
	Solving Equations with One Log Term
	Combining Operations
	The Ellipse
	Straight Lines
	Graphing Inequalities in Two Variables
	Solving Trigonometric Equations
	Adding and Subtracting Fractions
	Simple Trinomials as Products of Binomials
	Ratios and Proportions
	Solving Equations
	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
	Solving Quadratic Equations
	Dividing and Subtracting Rational Expressions
	Square Roots and Real Numbers
	Order of Operations
	Solving Nonlinear Equations by Substitution
	The Distance and Midpoint Formulas
	Linear Equations
	Graphing Using x- and y- Intercepts
	Properties of Exponents
	Solving Quadratic Equations
	Solving One-Step Equations Using Algebra
	Relatively Prime Numbers
	Solving a Quadratic Inequality with Two Solutions
	Quadratics
	Operations on Radicals
	Factoring a Difference of Two Squares
	Straight Lines
	Solving Quadratic Equations by Factoring
	Graphing Logarithmic Functions
	Simplifying Expressions Involving Variables
	Adding Integers
	Decimals
	Factoring Completely General Quadratic Trinomials
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Rational Expressions With Unlike Denominators
	Rational Exponents
	Horizontal and Vertical Lines

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Multiplying Fractions in General

Objective Learn how to multiply fractions.

Multiplying fractions is a little more difficult conceptually than adding fractions, but the arithmetic procedure is much easier. The discussion here will begin with the multiplication of a fraction by a whole number, proceed to the multiplication of two fractions each with numerator of 1, and then finish with the multiplication of any pair of fractions.

What if we want to multiply two fractions that do not have 1 as their numerators? The following procedure can be used to multiply any two fractions.

Key Idea

To multiply two fractions, multiply the numerators together to find the numerator of the product, and multiply the denominators together to find the denominator of the product. Simplify the resulting fraction, if possible.

Example 1

Why Does This Procedure Work?

We can draw a model. For example, to model the multiplication of and , we start with two line segments of the same length. Divide one segment into 3 equal parts and darken 2 of the parts. Divide the other segment into 5 equal parts and darken 2 of these parts.

The two segments are then used as adjacent sides of a square and the marks are used to divide the square into 15 regions of equal size. The region formed by the two darkened parts of the segments is then shaded.

The shaded portion of the entire square includes 4 of the 15 small regions of equal size. Since each small region represents the fraction , the shaded portion represents the fraction , which is the product of and .