 # From Ratio Tables to Equations Using the Value of the Ratio

Video solutions to help Grade 6 students learn how tto use the value of the ratio to problem-solve by writing and solving equations.

Lesson 13 Student Outcomes

• Students restate a ratio in terms of its value; e.g., if the ratio of length A to length B is 3:5 (in the same units), students state that “length A is 3/5 of length B”, “length B is 5/3 of length A”, “ length A is 3/8 of the total length”. and “length B is 5/8 of the total length".
• Students use the value of the ratio to problem-solve by writing and solving equations.

Lesson 13 Summary

The value of a ratio can be determined using a ratio table. This value can be used to write an equation that also represents the ratio.
The multiplication table can be a valuable resource to use in seeing ratios. Different rows can be used to find equivalent ratios.

Lesson 13 Exercises

Exercise 1
Jorge is mixing a special shade of orange paint. He mixed 1 gallon of red paint with 3 gallons of yellow paint. Based on this ratio, which of the following statements are true?
• 3/4 of a 4-gallon mix would be yellow paint.
• Every 1 gallon of yellow paint requires 1/3 gallon of red paint.
• Every 1 gallon of red paint requires 3 gallons of yellow paint.
• There is 1 gallon of red paint in a 4-gallon mix of orange paint.
• There are 2 gallons of yellow paint in an 8-gallon mix of orange paint.

Exercise 2
Based on the information on red and yellow paint, complete the table below.

Exercise 3
Jorge now plans to mix red paint and blue paint to create purple paint. The color of purple he has decided to make combines red paint and blue paint in the ratio 4:1. If Jorge can only purchase paint in one gallon containers, construct a ratio table for all possible combinations for red and blue paint that will give Jorge no more than 25 gallons of purple paint.

Exercise 3
a. Let B represent the number of gallons of blue paint, let R represent the number of gallons of red paint, and let T represent the total number of gallons of (purple) paint. Then write an equation that also models this relationship and answer the questions.
b. During a particular U.S. Air Force training exercise, the ratio of the number of men to the number of women was 6:1. Use the ratio table provided below to create at least two equations that model the relationship between the number of men and the number of women participating in this training exercise. Problem Set
A cookie recipe calls for 1 cup of white sugar and 3 cups of brown sugar. Make a table showing the comparison of the amount of white sugar to the amount of brown sugar.
1. Write the value of the ratio of the amount of white sugar to the amount of brown sugar.
2. Write an equation that shows the relationship of the amount of white sugar to the amount of brown sugar.
3. Explain how the value of the ratio can be seen in the table.
4. Explain how the value of the ratio can be seen in the equation.

Using the same recipe, compare the amount of white sugar to the amount of total sugars used in the recipe. Make a table showing the comparison of the amount of white sugar to the amount of total sugar.
5. Write the value of the ratio of the amount of total sugar to the amount of white sugar.
6. Write an equation that shows the relationship of total sugar to white sugar. Lesson 13 Word Problem

For each of the given ratio table, find the value of the ratio and the equation

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