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Ratios, Rates, Distance and Proportions

Ratios, Rates, Distance and Proportions. TSW write and simplify ratios. TSW determine unit rate. TSW calculate rates involving cost per unit to determine the best buy. DO NOW (not later):. Compare the number of boys to girls in the class. The number of boys = The number of girls =

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Ratios, Rates, Distance and Proportions

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  1. Ratios, Rates, Distance and Proportions TSW write and simplify ratios. TSW determine unit rate. TSW calculate rates involving cost per unit to determine the best buy.

  2. DO NOW (not later): • Compare the number of boys to girls in the class.

  3. The number of boys = • The number of girls = • If we compare boys to girls we get ___ boys to _____ girls.

  4. What do we call a comparison between two or more quantities? We just found the RATIO of boys to girls. RATIO Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.

  5. How many basketballs to footballs are there? • For every 4 basketballs there are 6 footballs. • The ratio is 4 to 6.

  6. What are some other ways we can write the ratio of basketball to footballs? • 4 to 6 • 4 : 6 • 4 6 Every ratio can be written in 3 ways: First quantity to Second quantity Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4 First quantity : Second quantity First quantity divided by the second quantity (as a fraction).

  7. Practice problem # 1 • You have 100 different shirts. There are 20 blue shirts and 80 black shirts. • a) Write the ratio of blue to black shirts 3 different ways. • b) Write the ratio in simplest form. • c) Explain what this ratio tells us. • d) How many black shirts do you have?

  8. Solution - # 1  a) Write the ratio of blue to black shirts 3 different ways. 20 to 80 , 20 : 80, 20 80 b) Write the ratio in simplest form.1 4 c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts. d) How many black shirts do you have? 1x + 4x = 100 5x = 100 x = 20 There are 4x black shirts so 2 (40) = 80 black shirts

  9. Practice Word Problems • Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy. • Explain what this ratio tell us.

  10. Rate • In a ratio, if the numerator and denominator are measured in different units then the ratio is called a rate. • A unit rate is a rate per one given unit, like 60 miles per 1 hour.

  11. Example: You can travel 120 miles on 6 gallons of gas. What is your fuel efficiency in miles per gallon. • 120 miles = 20 miles6 gallons 1 gallon • Your fuel efficiency is 20 miles per gallon.

  12. Unit Price • A unit rate involving money is a unit price. • Unit price is used to determine the best buy. • Example: A 24 ounce box of cereal costs $5.28. What is the unit price of the cereal? • Just divide 5.28 by 24. Therefore, you are paying $0.22 per ounce of cereal.

  13. Additional Example 4A: Finding Unit Prices to Compare Costs Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price? Divide the price by the number of pens. price for package number of pens $1.95 5 = = $0.39 price for package number of pens $6.20 15 =  $0.41 The 5-pack for $1.95 has the lower unit price.

  14. price for bottle number of ounces price for bottle number of ounces Check It Out! Example 4B John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price? Divide the price by the number of ounces. $2.19 24 =  $0.09 $3.79 36 =  $0.11 The 24 oz jar for $2.19 has the lower unit price.

  15. Determine the better buy! • Six rolls cost $0.90. • Twelve rolls cost $1.68. • Which is the better deal?

  16. Determine the better buy! • The big can held 16 ounces and cost 80 cents. • The small can held 12 ounces and cost 72 cents. • Which can was the better buy?

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