### About Ratios, Rates, & Proportions:

In math, a ratio is a comparison of two quantities. It’s used when we want to compare the quantity of one thing versus the quantity of something else. A rate is a special type of ratio where the comparison involves different units. Most often, we are looking for a unit rate. A unit rate is the amount of one thing when compared to a single unit of another. When two ratios or two rates are equal, they are known as a proportion.

Test Objectives

- Demonstrate the ability to find and write a simplified ratio
- Demonstrate the ability to find and write a simplified unit rate
- Demonstrate the ability to determine if two ratios represent a proportion
- Demonstrate the ability to solve proportion word problems

#1:

Instructions: Solve each problem.

a) State the ratio of apples to oranges

b) State the ratio of pineapples to apples

c) State the ratio of apples to oranges to pineapples

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#2:

Instructions: Solve each problem.

a) Global bakery sells muffins, which are created from a secret mixture. To create their secret mixture, they use a starter mixture, which contains 27 cups of flour for every 14 cups of sugar. If the starter mixture contains a total of 820 cups of both flour and sugar, how many cups of each are present?

b) The new model Z car has a 17.9-gallon fuel tank. Under optimum conditions, the car can travel 1074 miles on a full tank of gas. What is the mpg rating for this car under optimum conditions?

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#3:

Instructions: Solve each problem.

a) A new health mix is sold in a 54-ounce bulk container. The package contains a total of 1026 grams of protein. If one serving is half of an ounce, how many grams of protein are in each serving?

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#4:

Instructions: Determine if the following represents a proportion.

$$a)\hspace{.1em}\frac{5 \hspace{.2em}\text{apples}}{13 \hspace{.2em}\text{oranges}}? \frac{10 \hspace{.2em}\text{apples}}{20 \hspace{.2em}\text{oranges}}$$

$$b)\hspace{.1em}\frac{3 \hspace{.2em}\text{males}}{19 \hspace{.2em}\text{females}}? \frac{12 \hspace{.2em}\text{males}}{76 \hspace{.2em}\text{females}}$$

$$c)\hspace{.1em}\frac{30 \hspace{.2em}\text{pens}}{18 \hspace{.2em}\text{pencils}}? \frac{120 \hspace{.2em}\text{pens}}{90 \hspace{.2em}\text{pencils}}$$

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#5:

Instructions: Instructions: Determine if the following represents a proportion.

a) The scale of a local wall map is 2 inches: 59 miles. What is the distance on the map between Ronnan and Jeryville, two cities that are 678.5 miles apart?

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Written Solutions:

#1:

Solutions:

a) 2:1

b) 3:4

c) 4:2:3

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#2:

Solutions:

a) 540 cups of flour, 280 cups of sugar

b) 60 mpg (miles per gallon)

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#3:

Solutions:

a) 9.5 grams of protein per serving

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#4:

Solutions:

a) Not a proportion

b) Proportion

c) Not a proportion

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#5:

Solutions:

a) 23 inches