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7.1 ratios and rates 1

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7.1 ratios and rates 1

1. 1. Lesson 7.1 , For use with pages 343-346 Write the fraction in simplest form. 1. 14 21 2. 25 55
2. 2. Lesson 7.1 , For use with pages 343-346 Write the fraction in simplest form. 1. 14 21 2. 25 55 ANSWER 2 3 ANSWER 5 11
3. 3. 7.1 Ratios and Rates
4. 4. Essential Questions <ul><li>What is the connection between a ratio and a fraction? </li></ul><ul><li>Why are ratios and proportions important? </li></ul><ul><li>How are scale drawings, models, and proportions used in everyday life? </li></ul>
5. 5. Section 7.1 <ul><li>Vocabulary: </li></ul><ul><li>Ratio – a comparison of two quantities (like quantities) </li></ul><ul><li>3 ways to write a ratio (all read the same) </li></ul><ul><li>3 to 4 3 : 4 </li></ul>
6. 6. Ratios <ul><li>Ratios are similar to fractions because they </li></ul><ul><ul><li>1) can be written like a fraction </li></ul></ul><ul><ul><li>2) can be simplified like a fraction </li></ul></ul><ul><ul><li>3) compare two things Example: boys to girls in the classroom </li></ul></ul><ul><ul><li>12: 14 but can be simplified to </li></ul></ul><ul><ul><li>6: 7 ( for every 6 boys, there are 7 girls) </li></ul></ul>
7. 7. <ul><li>Vocabulary: </li></ul><ul><ul><li>RATE: a special kind of ratio in which quantities using different units are compared. </li></ul></ul><ul><ul><li>Example: 15 oranges for \$2.00 65 miles in one hour </li></ul></ul><ul><ul><li>\$300 for 10 books </li></ul></ul>
8. 8. <ul><li>Vocabulary: </li></ul><ul><li>Unit Rate : a comparison to 1 unit </li></ul><ul><li>(using the words like per mile, per minute, per inch – meaning in ONE) </li></ul><ul><li>Examples: 25 miles/gallon \$43 / book </li></ul><ul><li>82 cents / picture (meaning: for ONE of these items) </li></ul><ul><li>Name some other “unit rates”. </li></ul>
9. 9. <ul><li>Find the unit rate of each: </li></ul><ul><li>\$80 for 4 hour </li></ul><ul><li>500 words in 10 minutes </li></ul><ul><li>175 students for 5 teachers </li></ul>
10. 10. <ul><li>Tide detergent cost \$5.98 for 46 oz., while a 75 oz. box costs \$8.99. Which is the better buy? </li></ul><ul><li>When might a “larger” amount of some item not be the better buy? </li></ul>
11. 11. <ul><li>A proportion is an equation stating that two ratios are equal. </li></ul><ul><li>For example: </li></ul><ul><li>If cross products are equal, the ratios form a proportion. </li></ul>
12. 12. EXAMPLE 2 Using the Cross Products Property Write original proportion. Cross products property Multiply. Divide each side by 6.8 . Simplify. Check: You can check your solution by finding the cross products of the proportion. If the cross products are equal, the solution is correct. 6.8 15.4 = 40.8 m 6.8 m 6.8 = 628.32 6.8 m = 92.4 6.8 m = 15.4 (40.8) 6.8 m = 628.32
13. 13. EXAMPLE 2 Substitute 92.4 for m . Multiply. Using the Cross Products Property 6.8 (92.4) 15.4 (40.8) = ? 628.32 628.32 = ? 6.8 15.4 = 40.8 92.4
14. 14. GUIDED PRACTICE for Example 2 Solve the proportion. Then check your solution. Write original proportion. Cross products property Multiply. Divide each side by 54. Simplify. 5. 6 c = 54 99 6 (99) = 54c 594 = 54c 594 54 54c 54 = = 11 c 6 c = 54 99
15. 15. Check: Substitute 11 for m. Multiply. GUIDED PRACTICE for Example 2 6 (99) 11 (54) = ? 594 594 = ? 6 11 = 54 99
16. 16. GUIDED PRACTICE for Example 2 Solve the proportion. Then check your solution. Cross products property Multiply. Divide each side by 84. Simplify. Write original proportion. 6. n 14 = 63 84 84 n = 14(63) 84 n = 882 84 n 84 882 84 = = n 10.5 n 14 = 63 84
17. 17. GUIDED PRACTICE for Example 2 Check: Substitute 10.5 for m. Multiply. 10.5 (84) 14 (63) = ? ? 10.5 14 = 63 84 882 882 =
18. 18. GUIDED PRACTICE for Example 2 Solve the proportion. Then check your solution. Cross products property Multiply. Divide each side by 2.1. Simplify. Write original proportion. 7. 2.1 0.9 = 27.3 y 2.1 y = 0.9(27.3) 2.1 y = 24.57 2.1 y 2.1 24.57 2.1 = = y 11.7 2.1 0.9 = 27.3 y
19. 19. Check: Substitute 11.7 for m. Multiply. GUIDED PRACTICE for Example 2 (2.1) (11.7) 0.9 (27.3) = ? 24.57 24.57 = ? 2.1 0.9 = 27.3 11.7
20. 20. Homework <ul><li>Page 345 #19-26 </li></ul><ul><li>Page 351 #12-19 </li></ul>