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Solving Two-Step Equations Algebraically
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Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   

Ratios

A ratio compares two amounts. You can use ratios to compare numbers in different ways. For instance, you can compare part of a group to the whole collection: "Four out of five kids like math!"

Or, you can compare part of a group to another part: "For every four kids that like math, one more kid doesn't."

A ratio is the relationship between two numbers or values.

Writing Ratios in Simplest Terms

When the numbers in a ratio are large, it can be difficult to see the relation between them. It often helps to reduce a ratio to its simplest terms.

To write a ratio in simplest terms, divide both parts by their greatest common factor (GCF).

Reducing a ratio to simplest terms does not change the relationship between the numbers. Suppose a ratio of chocolate donuts to maple bars is 6:4. Notice there are three chocolate donuts for every two maple bars. We can reduce the ratio 6:4 to 3:2.

Reducing a ratio is very much like reducing a fraction.

Common Mistakes With Ratios

 Ã˜Warning: A common mistake with ratios is in choosing the term for the ‘total’. Read the problem carefully! Does it ask to compare a number to the total amount, or to the remaining amount?

Tying Them All Together

Ratios and fractions are interchangeable, and they can also be written as a decimal or a percent.

Percent Decimal Fraction Ratio
6% 0.06 6/100 0.06 : 1

or 3 : 50

Identifying Equal Ratios

Since a ratio is just another fraction, multiplying or dividing both terms by the same number does not change the ratio.

Example:

Are the ratios and equal?

Solution 1: Equivalent Fractions

common denominator = 12

So re-write the fractions using the common denominator:

ratios are not equal

Solution 2: Cross Product Test

Another way to compare ratios or fractions is to use the cross product test: This is usually the easiest way to compare fractions at a glance.

Multiply the numerator of one fraction by the denominator of the other. Do this for both fractions, and write the answers. If the two products are equal, then the fractions are equal.

ratios are not equal

Here’s another neat thing about the cross product test. It can easily tell you which fraction is larger! Just write the product above its numerator. Then compare the numbers in the same order you wrote them. For example:

the right hand ratio is larger

Solution 3: Decimal Comparison

Another way to compare ratios is to grab your calculator, and compute the decimal number.

10/15 = 0.6666666666667

12/16 = 0.75 ratios are not equal

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