1. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 4 Ratios and Proportions

2. 4-1-2 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Section 4.1 Understanding Ratios

3. 4-1-3 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Understanding a Ratio A ratio is the comparison of two quantities by division. The ratio of a to b can be written The quantities being compared are known as the terms of the ratio.

4. 4-1-4 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Write and Simplify a Ratio The ratio of a to b is generally written as We can also denote this ratio as a:b or by a to b. The order of the terms is important. The number mentioned first is the numerator of the fraction, the number before the colon, or the number before the word to. The number mentioned second is the denominator of the fraction, the number after the colon, or the number after the word to.

5. 4-1-5 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Write each ratio in three different ways. a.the ratio of 9 to 13 b.the ratio of 14 to 3

6. 4-1-6 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy 9:13 Write each ratio in three different ways. a.the ratio of 9 to 13 b.the ratio of 14 to 3 9 to 13 14:314 to 3

7. 4-1-7 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Simplifying a Ratio

8. 4-1-8 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Simplify each ratio. a.9 to 27 b.21 to 35 c.40 to 28

9. 4-1-9 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify each ratio. a.9 to 27 b.21 to 35 c.40 to 28

10. 4-1-10 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Simplify a Ratio that contains Decimals

11. 4-1-11 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Simplify the ratio 3.25 to 0.5.

12. 4-1-12 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify the ratio 3.25 to 0.5.

13. 4-1-13 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Simplify a Ratio that contains Fractions or Mixed Numbers

14. 4-1-14 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Simplify the ratio

15. 4-1-15 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify the ratio

16. 4-1-16 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Write a Ratio of Converted Measurement Units In ratios that compare measurement, the units must be the same. When we are given different units, we must rewrite the terms of the ratio using the same units. We can write the ratio in terms of either unit of measurement. Although the simplified ratio will be the same either way, as a general rule, it is easier to write the ratio with values in terms of the smaller measurement units. Here are some measurement conversion tables.

17. 4-1-17 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Time Measurement Conversion Table

18. 4-1-18 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Liquid Measurement Conversion Table

19. 4-1-19 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Linear Measurement Conversion Table

20. 4-1-20 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Weight Measurement Conversion Table

21. 4-1-21 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Simplify each ratio. Use values in terms of the smaller measurement units. a.15 hours to 3 days b.13 quarts to 6 pints c. 5 yards to 10 feet d.40 ounces to 4 pounds

22. 4-1-22 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify each ratio. Use values in terms of the smaller measurement units. a.15 hours to 3 days b.13 quarts to 6 pints

23. 4-1-23 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify each ratio. Use values in terms of the smaller measurement units. c. 5 yards to 10 feet d.40 ounces to 4 pounds

24. 4-1-24 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Apply your knowledge a.the ratio of red to yellow A small bag of M&Ms has 16 red, 14 blue, 12 yellow, and 8 orange M&Ms. Write each ratio in three different ways. Simplify, if possible. b.the ratio of blue to orange c.the ratio of orange to red d.the ratio of yellow to the total e.the ratio of the total to blue

25. 4-1-25 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy 4 to 3 a.the ratio of red to yellow A small bag of M&Ms has 16 red, 14 blue, 12 yellow, and 8 orange M&Ms. Write each ratio in three different ways. Simplify, if possible. 4:3

26. 4-1-26 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy 7 to 4 A small bag of M&Ms has 16 red, 14 blue, 12 yellow, and 8 orange M&Ms. Write each ratio in three different ways. Simplify, if possible. 7:4 b.the ratio of blue to orange

27. 4-1-27 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy 2 to 1 A small bag of M&Ms has 16 red, 14 blue, 12 yellow, and 8 orange M&Ms. Write each ratio in three different ways. Simplify, if possible. 2:1 c.the ratio of orange to red

28. 4-1-28 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy 6 to 25 A small bag of M&Ms has 16 red, 14 blue, 12 yellow, and 8 orange M&Ms. Write each ratio in three different ways. Simplify, if possible. 6:25 d.the ratio of yellow to the total

29. 4-1-29 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy 25 to 7 A small bag of M&Ms has 16 red, 14 blue, 12 yellow, and 8 orange M&Ms. Write each ratio in three different ways. Simplify, if possible. 25:7 e.the ratio of the total to blue