Section A Understanding Ratios and Proportions. 7-1 Ratios and Rates 7-2 Using Tables to Explore Ratios and Rates 7-4 Proportions.

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1 Section A Understanding Ratios and Proportions 7-1 Ratios and Rates 7-2 Using Tables to Explore Ratios and Rates 7- Proportions Section A Quiz 0

2 LESSON 7-1 Proportional Relationships Ratios and Rates Objective To write ratios and rates and to find unit rates Vocabulary ratio a comparison of two quantities using division Example 1 Writing Ratios You can compare the different groups by using ratios. For example, you can compare the number of violins with the number of violas. This ratio can be written in three ways to 29: Notice that the ratio of violins to violas, 29 order of the terms is important., is different from the ratio of violas to violins, 29. The Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part. Use the table above to write each ratio in three ways. A. flutes to clarinets part to part 5 or 5 to or 5: B. trumpets to total instruments or to 95 or :95 part to whole 95 C. total instruments to basses 95 or 95 to 9 or 95:9 9 whole to part 1

3 equivalent ratios ratios that name the same comparison You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number. Example 2 Writing Equivalent Ratios Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern. number of diamonds number of spades = rate a ratios that compares two quantities that have different units of measure unit rate a rate in which the second quantity in the comparison is one unit Example Consumer Math Application A -pack of paper towels costs $2.79. A 6-pack costs $5.6. Which is the better deal? $2.79 rolls Write the rate. $5.6 6 rolls Write the rate. $2.79 rolls Divide both terms by. $ rolls 6 Divide both terms by 6. $0.9 1roll $0.9 for 1 roll. $0.91 1roll $0.91 for 1 roll. The 6-pack is the better deal. Homework: p. 288: 1-11, -20 even 2

4 LESSON 7-2 Proportional Relationships Using Tables to Explore Equivalent Ratios and Rates Objective To use a table to find equivalent ratios and rates Example 1 Making a Table to Find Equivalent Ratios Use a table to find three equivalent ratios. A. 8 original 8 x 2 8 x 8 x ratio x 2 x x Multiply the numerator and the denominator by 2,, and The ratios,,,and are equivalent B. 0 to 16 Divide the numerator and denominator by 2,, and 8. original ratio The ratios C. : ,,, 16 8 and 5 2 are equivalent. original x 2 x x ratio x 2 7 x 7 x The ratios, 8, 16, and are equivalent

5 Example 2 Entertainment Application A. Several groups of friends are going to take a shuttle bus to the park. The table shows how much the different groups will pay in all. Predict how much a group of 15 friends will pay. Number in Group 6 18 Bus Fare ($) 2 6 < 15 < 18; therefore the group will pay between $2 and $6. The ratio 6 is equivalent to, and is a factor of = 15 Multiply the numerator and denominator by the same factor, 5. 5 $6 = $0 A group of 15 friends would pay $0. B. A group of 10 friends is in line to see a movie. The table shows how much different groups will pay in all. Predict how much the group of 10 will pay. Number in group 5 6 Amount Paid ($) A. 1 person 10 people $5 $50 or B. 5 people 10 people $25 $50 Homework: p. 292: 1-9 odd, even

6 LESSON 7- Proportional Relationships Proportions Objective To write and solve proportions Vocabulary proportion an equation that shows two equivalent ratios Example 1 Modeling Proportions Write a proportion for the model. First write the ratio of triangles to circles. number of triangles number of circles 2 Next separate the triangles and circles into two equal groups. Now write the ratio of triangles to circles in each group. number of triangles in each group number of circles in each group 2 1 A proportion shown by the model is

7 Example 2 Using Cross Products to Complete Proportions A. Find the missing value in the proportion n 16. n 16 Find the cross product. n = 16 The cross products are equal. n = 8 n = Divide both sides by to undo the multiplication. Find the missing value in each proportion. B. 9 n C. t D. 1 6 c E b 9n 20t c 1 6b 7 0 9n 6 20t 10 6c 6b 210 n t 7 c 2 b 5 6

8 Example Measurement Application The label from a bottle of pet vitamins shows recommended dosages. What dosage would you give an adult dog that weighs 15 lb? 1 tsp v = 20 lb 15 lb 20v v 15 20v v 0.75 tsp. 7 Homework: p. 0: 1-, 1-20 even, 22, 2