2. 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.

3. DO NOW (not later): CCompare the number of boys to girls in the class.

4. TThe number of boys = TThe number of girls = IIf we compare boys to girls we get ___ boys to _____ girls.

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

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

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

8. 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?

9. 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

10. Practice Word Problems (1)Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy. (2)Explain what this ratio tell us.

11. 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.

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

13. 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.

14. 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? Additional Example 4A: Finding Unit Prices to Compare Costs 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.

15. 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?  $2.19 24 = $0.09 = $3.79 36  $0.11 The 24 oz jar for $2.19 has the lower unit price. price for bottle number of ounces price for bottle number of ounces Divide the price by the number of ounces.

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

17.  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? Determine the better buy!