Introduction to Proportions & Using Cross Products

Lesson 6-3 & 6-4

CCS: 6.RP.3. Use Proportional reasoning to solve real-world and mathematical problems6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

• Objectives:• Students will be able to:

– Test Ratios and Proportions– Complete and Identify Proportions– Use cross multiplication to solve

proportions

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.

Video Explanations for Proportions• Identifying Proportions

Examples: Do the ratios form a proportion?

710

, 2130

x 3

x 3

Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators.

89

, 23

÷ 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

3540 =

7

÷ 5

÷ 5

8

Video for Examples Using Cross Products

• Cross Products Proportional Relationships

• Using Mental Math to Solve Proportions

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.

412

, 39

12 x 3 = 369 x 4 = 36

These two ratios DO form a proportion because their cross products are the same.

Example 2

58

, 23

8 x 2 = 163 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

k17

=2068

Start with the variable.

=68k 17(20)

Simplify.

68k = 340

Now we have an equation. To get the k by itself, divide both sides by 68.

68 68

k = 5

Classwork: Play Dirt Bike Proportions to practice solving proportions. You can play against up to 3 friends!

Try this interactive math lesson to solve proportions.

Homework Time- 6-3 & 6-4 Handout