Welcome to this IRSC Adult Education Live Virtual Lesson Diana Lenartiene, Ed. S. moderator/instructor

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Ratios We will now view a video on Ratio

Ratios A ratio is a comparison between two numbers by division. It can be written in three different ways: 5 to 2 5 : 2 5 2

Equal Ratios When two ratios name the same number, they are equal. It ’ s like writing an equivalent fraction. 20 : 30 Equal Ratios: 10 : 15 2 : 3 80 : 120

Ratios in Simplest Form Ratios can be written in simplest form. Divide both terms in the ratio by their GCF. Example: 12 to 8 3 to 2 12/8 = 3/2 We have reduced the fraction to lowest terms. To do that, we divided the numerator and denominator by 4.

Understanding Proportions We will now watch a video on proportion

Vocabulary A proportion is an equation stating that two ratios are equal. To prove that two ratios form a proportion, you must prove that they are equivalent. To do this, you must demonstrate that the relationship between numerators is the same as the relationship between denominators.

Examples: Do the ratios form a proportion?, x 3 Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators. 8 9, 2 3 ÷ 4 ÷ 3 No, these ratios do NOT form a proportion, because the ratios are not equal.

Completing a Proportion Determine the relationship between two numerators or two denominators (depending on what you have). Execute that same operation to find the part you are missing.

Example: Cross multiply to see if they are equal! 3= Multiply 3 x 8 = 24 Multiply 4 x 7 = 28 These ratios are NOT a proportion! Why? Because they were not equal

Using Cross Products

Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross product by multiplying the denominator of each ratio by the numerator of the other ratio.

Example: Do the ratios form a proportion? Check using cross products. 4 12, x 3 = 36 9 x 4 = 36 These two ratios DO form a proportion because their cross products are the same.

Example 2 5 8, x 2 = 16 3 x 5 = 15 No, these two ratios DO NOT form a proportion, because their cross products are different.

Solving a Proportion Using Cross Products Use the cross products to create an equation. Solve the equation for the variable using the inverse operation.

Example: Solve the Proportion k 17 = Start with the variable. =68 K 17(20) Simplify. =340 Now we have an equation. To get the k by itself, divide both sides by 68. k = 5 68 K 68

We will now view a video showing how to Set up and solve word problems using the Proportion formula.

 A ratio shows the relation ship of tow things as a Fraction.  A proportion is a statement that two ratios are equal  Proportions allow us to solve problems by using the Proportion formula.  We can set up proportions to solve real world math Problems.

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Thank you for viewing this presentation. Diana Lenartiene, IRSC ABE Instructor If you still have questions, please contact me at: