DO NOT WRITE RATIOS AS MIXED NUMBERS. NOTE THAT THE ORDER MATTERS.

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1 Math 20 Arithmetic Sec 5.1: Ratios Defn A ratio compares two quantities that have the same type of units. A rate compares two quantities with different units. Ex Suppose the ratio of your monthly expenses to your monthly income is 10 to 9. What does this mean? Suppose the ratio is 9 to 10? Is this favorable? Notation The ratio 10 to 9 can be expressed the following ways: or DO NOT WRITE RATIOS AS MIXED NUMBERS. NOTE THAT THE ORDER MATTERS. Ex 1 Shane spent $14 on meat, $5 on milk, and $7 on fresh fruit. Write each ratio as a fraction. a) The ratio of the amount spent on fruit to amount spent on milk. b) Prac Prob The ratio of the amount spent on milk to amount spent on meat. c) The ratio of the amount spent on meat to amount spent on milk. Ex 2 Write each ratio as a fraction in lowest terms. a) 100 meters to 50 meters b) The price of Tamar s favorite brand of lipstick increased from $5.50 to $7.00. Find the ratio of the increase in price from the original price. c) Last week, Lance worked 4.5 hours each day. This week he cut back to 3 hours each day. Find the ratio of the decrease in hours to the original number of hours. Ex 3 Write each ratio as a ratio of whole numbers in lowest terms. a) to b) to Page 1 of 8

2 Ex 4 Write each ratio as a fraction in lowest terms. NOTE: It is usually easier to write the ratio using the smaller measurement unit. The provided table can be found on pg 320. a) 9 in. to 6 ft. Measurement Comparisons Length Capacity 1 foot = 12 inches 1 pint = 2 cups 1 yard = 3 feet 1 quart = 2 pints 1 mile = 5280 feet 1 gallon = 4 quarts Weight Time 1 pound = 16 ounces 1 minute = 60 seconds 1 ton = 2000 pounds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days b) 2 days to 8 hours c) 3 quarts to 3 gallons Ex 5 (#44) The price that a pharmacy pays for an antibiotic decreased from $8.80 to $5.60 for 10 tablets. Find the ratio of the decrease in price to the original price. What does this ratio represent? Sec 5.2: Rates Recall Defn A ratio compares two quantities that have the same type of units. A rate compares two quantities with different units. NOTE: per means divide Ex 6 Write each rate as a fraction in lowest terms. a) $6 for 30 packages b) 500 miles in 10 hours c) Prac Prob 4 teachers for 90 students Page 2 of 8

3 Ex 7 Find the unit rate. a) $4.35 for 3 pounds of cheese b) 24-lb turkey for 15 people Ex 8 Find the best buy (lowest cost) for the purchase. 6 cans of cola for $ cans of cola for $ cans of cola for $7 Unit Rate for 6-can purchase Unit Rate for 12-can purchase Unit Rate for 24-can purchase Ex 9 Which tube of toothpaste is a better buy? You have a coupon for 85 cents off Brand C and a coupon for 20 cents off Brand D. Brand C is $3.89 for 6 ounces Brand C Price Brand D is $1.59 for 2.5 ounces Brand D Price Page 3 of 8

4 Ex 10 (#36) Calculator Two brands of facial tissue are available. Brand K is specially priced at three boxes of 175 tissues each for $5. Brand S is priced at $1.29 per box of 125 tissues. You have a coupon for 20 off one box of Brand S and a coupon for 45 off one box of Brand K. How can you get the best buy on one box of tissue? Sec 5.3: Proportions Defn A proportion states that two ratios or rates are equivalent. Ex 11 Write each proportion. a) $7 is to 3 cans as $28 is to 12 cans b) 9 meters is to 16 meters as 18 meters is to 32 meters Ex 12 Determine whether each proportion is true or false by writing both ratios in lowest terms. a) b) PP c) PP Alternative Method Another way to determine whether a proportion is true or false is by using cross products. If the cross products are equal, the proportion is true. Otherwise, it is false. Page 4 of 8

5 Ex 13 Find the cross-products to see whether each proportion is true or false. a) b) c) PP d) PP e) f) g) Page 5 of 8

6 Sec 5.4: Solving Proportions We will use variables (letters) in place of unknown numbers. Sometimes a? is used. Ex 14 Find the unknown numbers. First find the exact answer. Next, round to the hundredths when necessary. Check your solution by finding the cross products. a) b) c) d) e) f) g) h) Page 6 of 8

7 i) j) Sec 5.5: Solving Application Problems with Proportions Set up and solve each proportion problem. Ex 15 (#4) Twenty-two guitar lessons cost $396. Find the cost of 12 lessons. Ex 16 (#12) One gallon of clear gloss wood finish covers about 550 square feet of surface. If you need to apply three coats of finish to 400 square feet of surface, how many gallons do you need, rounded to the nearest tenth? Ex 17 (#14) Use the floor plan to answer the following: What is the actual length and width of the entire family room? On the plan, one inch represents four feet. Page 7 of 8

8 Ex 18 (#22) In a test of 200 sewing machines, only one had a defect. At that rate, how many of the 5600 machines shipped from the factory had defects? What happens if we had the incorrect setup (used reciprocal instead)? Ex 19 (#28) The Rosebud School District wants a student-to-teacher ratio of 9 to 1. How many teachers are needed for 1850 students? Round to the nearest whole number. Ex 20 (#38) A -cup serving of penne pasta has 210 calories and 2 grams of dietary fiber. How many calories and grams of fiber will be in a 1-cup serving? Page 8 of 8