Equivalent Ratios
Opening Activity
Name _______________________________________
You are making homemade hand lotion and you find three recipes. Do the recipes make the same lotion? How can you tell?
Recipe 1 Recipe 2 Recipe 3
Melt these ingredients over low heat:
2/3 cup of apricot oil
1/3 cup of cocoa butter
1 teaspoon lanolin
½ ounce beeswax
When cool, add:
2/3 cup rosewater
1/3 cup aloe vera gel
2 drops rose oil
1 Vitamin E capsule
Mix together until a smooth lotion is formed.
Melt these ingredients over low heat:
1 cup of apricot oil
½ cup of cocoa butter
1 ½ teaspoons lanolin
¾ ounce beeswax
When cool, add:
1 cup rosewater
½ cup aloe vera gel
3 drops rose oil
1 ½ Vitamin E capsules
Mix together until a smooth lotion is formed.
Melt these ingredients over low heat:
1 ½ cups of apricot oil
2/3 cup of cocoa butter
2 teaspoons lanolin
1 ounce beeswax
When cool, add:
1 ½ cups rosewater
2/3 cup aloe vera gel
4 drops rose oil
2 Vitamin E capsules
Mix together until a smooth lotion is formed.
Write each as a ratio in simplest form.
1.
3 out of 12 people live in a rural area.
2.
98 homes in 100 have a TV.
3.
70 homes out of 125 have a personal computer.
4.
In one class, there are 6 girls for every 10 boys.

Equivalent Ratios
Lesson – Day 1
Name _______________________________________
1. A train traveling from St. Louis to Chicago travels 120 miles in 2 hours. Complete the rate table.
Distance (mi) 120 150 240
Time (hr) 2 3 5
2. Write the information in the table as a set of ordered pairs. Use Time as the x-coordinate and
Distance as the y-coordinate. Graph the ordered pairs.
(________ , ________)
(2, 120)
(________ , 150)
(3, ________)
(________ , 240)
(5, ________)
3. Describe your graph: ____________________________________________________________________________.
4. For each ordered pair in #2, write the ratio of the y-coordinate to the x-coordinate.
5. How far does the train travel in 1 hour? ____________________________ This is the train’s speed.
How is this related to the ratios you wrote in #4?
6. Explain how you can use the graph to find out how far the train traveled after 4.5 hours.

Equivalent Ratios
Lesson – Day 2
Name ________________________________
Keesha is making lemonade. Her recipe calls for 3 cups of lemon juice and 5 cups of water.
Brooke is also making lemonade. Brooke’s recipe calls for 2 cups of lemon juice and 3 cups of water.
1. In Keesha’s recipe, the ratio of lemon juice to water is __________________________.
Complete the table with equivalent ratios.
Lemon Juice (c) 3 9 12
Water (c) 5
2. Write the ratios for Keesha’s recipe as a set of ordered pairs using lemon juice for the xcoordinate and water for the y-coordinate.
(3, 5)
3. In Brooke’s recipe, the ratio of lemon juice to water is __________________________.
Complete the table with equivalent ratios.
Lemon Juice (c) 2 4
Water (c) 3 9 15
4. Write the ratios for Brooke’s recipe as a set of ordered pairs using lemon juice for the x-coordinate and water for the y-coordinate.
5. In each table, there is a column in which the amount of water is the same. Circle these columns.
6. Examine these two columns. Whose recipe makes stronger lemonade? Explain.

7. Graph the order pairs from #2 and #4. Use two different colors. What do you notice about the graphs?
8. The ratio of lemon juice to water in the stronger is ________________________ more than the ratio of lemon juice to water in the other recipe.
9. Use inequality symbols to compare the ratios:
10
15
9
15
 
2
3
3
5
 

Equivalent Ratios
Problem Solving
Name ________________________________
1.
During a checkers game, there are 16 pieces left. The ratio of black to red is 3:5. How many black pieces are on the board? Explain.
2.
Find the ratio of the length of the small rectangle to the length of the large rectangle.
Repeat this for the width, perimeter and area. Compare and contrast the ratios.
3.
There are 12 boys and 10 girls in your gym class. If 6 boys joined the class, how many girls would need to join for the ratio to remain the same?
4.
Describe and correct the error in writing an equivalent ratio. a.
2
3

2

2
3

3

4
9 b.
2
3

2

4
3

4

6
7
 
5.
Create three different drawings showing a number of circles and triangles in which the ratio of circles to triangles is 2:3.
6.
The number of cats in a neighborhood is 4 more than the number of dogs. The ratio of cats to dogs is 3:2. How many cats are in the neighborhood?