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Saturday 13th of July
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
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Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
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
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
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
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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Ratios and Proportions

Objective Learn the concepts of ratio and proportion and to solve proportion problems.



Mathematically, a ratio is simply a fraction viewed as a division of two numbers. Its importance is that it is used to compare two numbers (the numerator and the denominator of the fraction). For example, the ratio of x to y is simply the fraction . A ratio can also be written as x to y or x:y.

In the following example you can see how a ratio compares two numbers.


Example 1

In Ms. Cunningham's class there are 18 girls and 14 boys. Write the ratio of boys to girls.


The ratio of boys to girls in the class can be written as 14 to 18 or 14:18 or When simplified, this ratio can also be expressed as 7 to 9 or 7:9 or



An equation that states that two ratios are equal is called a proportion. The equation is a proportion. This proportion can also be written as 14:18 = 7:9

More generally a proportion will often involve variables. Solving these problems usually involves elementary algebra, because they involve solving for the value of a variable. To solve these kinds of problems we use a process called cross multiplying. The cross multiplying fact should be explained carefully to your students.

Cross Multiplication Fact Suppose 0 y and 0 b are not zero. Then occurs exactly when xb = ya.

Example 1

Solve for a .


Use the cross multiplication fact and solve the resulting equation.

3(15) = 5( a )

45 = 5a

9 = a


Why is the cross multiplication fact true?

Notice that occurs exactly when . Subtract these fractions by finding a common denominator.

occurs exactly when .

Remember that a fraction equals 0 only when its numerator equals 0. So for this equation, when xb - ya = 0 or when xb = ya. This is the result of cross multiplying .

The above discussion about why the cross multiplication fact is true is a very important example of mathematical reasoning. Namely, it uses a computational technique (subtraction of fractions) to derive a general principle (cross multiplication fact). In order to solidify this concept you should do many examples of how this technique is applied.

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