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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Using Proportions and Cross-Multiplication

Ratios are a powerful tool in science and math. But in order to take full advantage of them, we have to do more than just calculate ratios—we have to put them to work! For example, if you have three bacteria specimens for every student in your class, you know that you will have a ratio of 3 to 1, , or 3:1. But this ratio does not tell you the total number of specimens. To find that, you need to use a proportion.

A proportion is a statement of equality between two ratios. This means that the ratios are equal. It also means that the numerator of one ratio multiplied by the denominator of the other ratio is equal to the product of the other numerator and denominator. An example looks like this:

Notice that you are multiplying across the equal sign in your proportion. This process is called cross-multiplication. Cross-multiplication is useful because if you know three of the quantities in a proportion, you can find the fourth.

PROCEDURE: To find an unknown quantity in a proportion, set up the numbers you know in equal ratios. Leave the place for the quantity you do not know empty for now. Then cross-multiply the known numerator of one ratio with the known denominator of the other. Then divide this product by your remaining known quantity. The quotient is your answer.

SAMPLE PROBLEM: Find the missing number in this proportion:

Step 1: Cross-multiply the known numerator of one ratio with the known denominator of the other ratio.

Step 2: Divide this product with your remaining known quantity.

The missing number in the proportion is 25;

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