1 / 19

7-2

Using Tables to Explore Equivalent Ratios and Rates. 7-2. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Warm Up Find the unit rate. 1. 16 miles in 4 hours 2. 3 oranges for $2.40 3. 3 bottles for $0.93 4. 6 DVDs for $36.60. 4mi/h. $0.80 per orange. $0.31 per bottle.

mckile
Download Presentation

7-2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Using Tables to Explore Equivalent Ratios and Rates 7-2 Course 1 Warm Up Problem of the Day Lesson Presentation

  2. Warm Up Find the unit rate. 1.16 miles in 4 hours 2. 3 oranges for $2.40 3. 3 bottles for $0.93 4. 6 DVDs for $36.60 4mi/h $0.80 per orange $0.31 per bottle $6.10 per DVD

  3. Problem of the Day There are 4 ounces in a gill. There are 4 gills in a pint. There are 8 pints in a gallon. How many ounces are the same as the total of 3 gallons, 3 pints, 3 gills, and 3 ounces? 447

  4. Learn to use a table to find equivalent ratios and rates.

  5. Reading Math Finding equivalent ratios is sometimes referred to as “scaling up” or “scaling down.”

  6. Use a table to find ratios equivalent to 3 to 2. Original Ratio 3 • 2 3 • 3 3 • 4 2 • 2 2 • 3 2 • 4 You can increase amounts but keep them in the same ratio by multiplying both the numerator and denominator of the ratio by the same number. The ratios 3 to 2, 6 to 4, 9 to 6, and 12 to 8 are equivalent. You can also decrease amounts in the same ratio by dividing the numerator and denominator by the same number.

  7. 6 24 18 12 6 __ __ ___ ___ ___ 7 28 21 14 7 Additional Example 1A: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. Original Ratio 6 • 2 6 • 3 6 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 12 18 24 14 21 28 7 • 2 7 • 3 7 • 4 The ratios , , , and are equivalent.

  8. Helpful Hint Multiplying by 2, 3, and 4 will give you three equivalent ratios, but there are many other equivalent ratios that are correct.

  9. Additional Example 1B: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 3 to 5 Original Ratio 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 6 9 12 10 15 20 5 • 2 5 • 3 5 • 4 The ratios 3 to 5, 6 to 10, 9 to 15, and 12 to 20 are equivalent.

  10. Additional Example 1C: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 48:36 Original Ratio 48 ÷ 4 48 ÷ 2 48 ÷ 3 Divide the numerator and the denominator by 2, 3, and 4. 24 16 12 9 18 12 36 ÷ 4 36 ÷ 2 36 ÷ 3 The ratios 48:36, 24:18, 16:12, and 12:9 are equivalent.

  11. 3 12 9 6 3 __ __ ___ ___ ___ 8 32 24 16 8 Check It Out: Example 1A Use a table to find the equivalent ratios. Original Ratio 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 6 9 12 16 24 32 8 • 2 8 • 3 8 • 4 The ratios , , , and are equivalent.

  12. Check It Out: Example 1B Use a table to find the equivalent ratios. 2 to 9 Original Ratio 2 • 2 2 • 3 2 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 4 6 8 18 27 36 9 • 2 9 • 3 9 • 4 The ratios 2 to 9, 4 to 18, 6 to 27, and 8 to 36 are equivalent.

  13. Check It Out: Example 1C Use a table to find the equivalent ratios. 36:12 Original Ratio 36 ÷ 4 36 ÷ 2 36 ÷ 3 Divide the numerator and the denominator by 2, 3, and 4. 18 12 9 3 6 4 12 ÷ 4 12 ÷ 2 12 ÷ 3 The ratios 36:12, 18:6, 12:4, and 9:3 are equivalent.

  14. Additional Example 2: Application 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. 12< 15 < 18; therefore, the group will pay between $24 and $36.

  15. Additional Example 2 Continued Use the amount paid by the group of 6. Divide the bus fare by the number in each group to find the amount paid per person. 12 ÷ 6 = 2 2 • 15 = 30 Multiply. A group of 15 friends will pay $30 in bus fare.

  16. Check It Out: Example 2 Several groups of friends are purchasing tickets to an amusement park. The table shows how much the different groups will pay in all. Predict how much a group of 7 friends will pay. 6 < 7 < 8; therefore, the group will pay between $30 and $40.

  17. Check It Out: Example 2 Continued Use the amount paid by the group of 8. Divide the ticket prices by the number of people in each group to find the amount paid per person. 40 ÷ 8 = 5 5 • 7 = 35 Multiply. A group of 7 friends will pay $35 for amusement park tickets.

  18. , , , , , , 2 4 6 3 2 1 9 27 12 36 18 1 __ __ __ __ __ __ __ __ __ __ __ __ 60 4 6 9 12 8 16 3 5 30 10 12 Lesson Quiz: Part I Use a table to find three equivalent ratios. Possible Answers: 1. 2. 3.

  19. Lesson Quiz: Part II 4.Fred is saving for a new sound system. The table shows some amounts he could save in different numbers of weeks. Predict the amount of his savings after 10 weeks. $125

More Related