Instructions for Ratios and Proportions

A ratio is used to show a relationship between two numbers. The numbers are separated by a colon ( : ) as in 1:2.

The relationship can represent something as simple as the 1:3 ration commonly used to mix frozen juices. We use 1 can of frozen juice concentrate to 3 cans of water. This is an example of a part-to-part ratio. You can also have part-to-whole ratios. For example, the ratio of frozen juice concentrate to reconstituted juice is 1:4, that is, 1 can of concentrate to four cans of total reconstituted juice.

Proportions are two equivalent ratios in which the terms of the first ratio have the same relationship as the terms of the second ratio. For example, 1 cup of butter to 3 cups of sugar (1:3) is in proportion to 2 cups of butter to 6 cups of sugar (2:6). The easiest way to visualize proportions is to write the ratios in fraction form, like this:        Notice that in this proportion, the butter is on top, and the sugar on the bottom in both ratios. This is a helpful way to check that you are setting up a proportion correctly.

To solve for an unknown number in a proportion, you cross multiply, like this:

So let’s say that you are using a recipe of 2 teaspoons of vanilla for 3 cups of sugar. If you want to change the recipe so that it uses   cups of sugar, how much vanilla would you use?

2   = 3  

9 =

3  

You would use 3 teaspoons of vanilla.

If 12 eggs cost $1.49, how much to 18 eggs cost?

If one can serves 2.5 people, how many cans serve 10 people?

Sometimes proportions that contain fractions can be confusing, but they are solved in exactly the same way:

One way we use proportions in cost analysis is by finding the unit rate and seeing which of two options would be the better buy. Let’s say one store has a 24-ounce jar of spaghetti for $6.55, and another store has a 45-ounce jar for $13.40. Which is the better buy? What you would do is find the unit price for each jar. The first jar:

1   $6.55 = 24 ounces ?                                         1   $13.40 = 45 ounces   ?                           

$6.55 = 24 ounces   ?                                               $13.40 = 45 ounces   ?

$0.272 . . . = ?                                                               $0.297 . . . = ? 

1 ounce of spaghetti sauce =                                     1 ounce of spaghetti sauce=

27 cents (round to the nearest hundredth)            30 cents (round to the nearest hundredth)

The 24-ounce jar is the better buy!

Note: In this class we will always round answers to the nearest hundredth. To do that, you first have to determine where the hundredths place is, shown in red below. The next place over, in green, and beyond that, will drop out. The hundredths place number will either stay the same or increase by one. It is the number in the thousandths place, in green, that determines that. If the number in green is 0-4, the number in red stays the same. If the number in green is 5-9, the number in red increases by one.

4.367    4.37        0.211     0.21        21.0175     21.02         6.195    6.20        4.497     4.50

Notice for the last two, you add 1 to the 9 and it carries over to the next place. You would keep the 0 in this case.        

Assignment

Purpose

Outcomes

Instructions

Tips for Success

Ratios and Proportions Assignment

1) If you are using a recipe that has the proportion of 1 cup of butter to 3 cups of sugar, how many cups of butter will you need if you will be using 8 cups of sugar?

2) Maria is going to make a salad dressing that has the proportion of 3 tablespoons of olive oil to 1 tablespoon of lemon juice. If she wants to use 4 tablespoons of lemon juice, how much olive oil should she use?

3) I want to make a barbecue sauce that has the proportion of cup of packed brown sugar to cup apple cider vinegar. How much brown sugar should I use if I use   cups of vinegar?

4) Yesenia is going to make a salmon glaze that has the proportion of 2 tablespoons of lemon juice to   cup of soy sauce. How many cups of soy sauce should she use if the uses 3 tablespoons of lemon juice?

5) Mitch has a recipe for cake icing that has the proportion of 3 cups of confectioners sugar to cup of butter. How much butter should he use if he uses   cups of confectioners sugar?

6) The recipe has the proportion of 1 tablespoon of soy sauce to 3 pounds of chicken wings. How many pounds of chicken wings should you use if you want to use   tablespoons of soy sauce?

7) If a dozen eggs costs $1.60, how much would 8 eggs cost?

8) If a dozen doughnuts costs $8.99, how much would 18 doughnuts cost?

9) If 6 cans of soda cost $2.75, how much would 24 cans of soda cost?

10) If 8 bakery cookies cost $14, how much would 12 bakery cookies cost?

11) If a dozen dinner rolls cost $3.99, how much would 32 rolls cost?

12) If 8 deli fried chicken legs cost $8.72, how much would 6 chicken legs cost?

13) If a 19-fluid ounce bottle of dish soap costs $2.89, and a 40-fluid ounce bottle costs $5.79, which one is the better buy?

14) If a 32-fluid ounce bottle of lemon juice costs $3.29, and a 48-fluid ounce bottle costs $6.99, which one is the better buy?

15) If a 20-ounce bottle of ketchup costs $2.99, and a 32-ounce bottle of ketchup costs $3.19, which one is the better buy?

16) If a 29-ounce can of peaches costs $2.99, and a 15-ounce can of peaches costs $1.89, which one is the better buy?

17) If a 2-pound bag of flour costs $1.89, and a 5-pound bag of flour costs $3.86, which one is the better buy?

18) If a 26-ounce canister of salt costs $0.99, and a 64-ounce box of salt costs $1.69, which one is the better buy?