Mastering Proportions and Rates in Mathematics

1. Do Now 2/9/10 • Take out HW from last night. • Text p. 272, #10-36 evens, #44, & #47 • Copy HW in your planner. • Text p. 278, #10-30 evens, #35 • In your notebook, use the following unit rates to answer the following questions. If you are walking 5 meters in 1 second, how many meters will you walk in a hour? If you can buy 3 pounds for a $1, how many ounces can you buy for a $1?

2. Writing Equivalent Rates If you are walking 5 meters in 1 second, how many meters will you walk in a hour? If you can buy 3 pounds for a $1, how many ounces can you buy for a $1? There are 60 seconds in a minute and 60 minutes in a hour, so multiply 5 meters by 3600. There are 16 ounces in a pound, so multiply 3 pounds by 16.

3. 10) No; 3 to 4; 3/4, 3:4 12) No; 5 to 1; 5/1; 5:1 14) No; 7 to 2; 7/2; 7:2 16) Yes; 64 to 3; 64/3; 64:3 18) 4/2, 11 to 2, 36:5, 22:3, 30/4 20) 1/2, 6:10, 7:11, 8:12, 7:4 22) 35 words / 1 minute 24) 32 oz / 1 serving 26) $80 / 1 person 28) 1 3/5 muffins / $1 30) 79,200 32) 23,400 34) 301 36) a. 4/1 b. That the adult frog is 4 times smaller than the tadpole 44) 1/3 47) 1 1/11 minutes HomeworkText p. 272, #10-36 evens, #44, & #47

4. Objective • SWBAT write and solve proportions

5. RATIO- uses division to compare two quantities of the SAME MEASURE. RATE – a fraction in which the numerator and the denominator have different units of measure.

6. Proportion- Section 6.2 “Writing and Solving Proportions” an equation that states that two ratios/rates are equivalent. “a is to b as c is to d”

7. Solving a Proportion • Solve a proportion by finding the value of the variable. • One way to solve a proportion is to write both fractions with the same denominator (think of equivalent fractions). You need to find a value of n so that is equivalent to = =

8. 330 . x x x 11 Solve the proportion = = 30 30 30 6 6 x = 11 11 6 6 30 30 = Use Algebra to Solve Proportions How can we get ‘x’ by itself? Write original proportion. Multiply each side by 30. Simplify. 55= x Divide.

9. 24 . 2 2 2 x Solve the proportion = = 8 8 12 8 8 x x 12 12 12 12 = Try It Out… How can we get ‘x’ by itself? Write original proportion. Multiply each side by 12. Simplify. x = Divide. x = 3

10. Solve the Following Proportions: = = = = = =

11. Solving Equations with Rates • A punch recipe calls for 4 cups of orange juice. The recipe will serve 8 people. You are making punch for a party of 32 people. How many cups of orange juice do you need? =

12. Solving Equations with Ratios • You are making a scale drawing of a room. The actual room has a width of 18 ft and a length of 24 ft. Your scale drawing of the room has a length of 4 in. What is the width of the room on the scale drawing? =

13. Homework Text p. 278, #10-30 evens, #35