In this Grade 6 lesson from Saxon Math Course 1, students learn how to solve ratio problems using a constant factor, which is found by dividing or multiplying the actual count by the corresponding ratio number. Using a ratio box to organize information, students practice setting up and solving proportional relationships such as comparing quantities of paint colors or flowers to weeds. This lesson is part of Chapter 8 and builds students' foundational skills in proportional reasoning.
Section 1
📘 Using a Constant Factor to Solve Ratio Problems
Ratio numbers and actual counts are related by a constant factor.
Next, you'll use a ratio box to find this constant factor and solve problems involving everything from paint mixtures to garden weeds.
Section 2
Setting up a ratio box
A ratio box organizes information by separating the numbers in a ratio from the actual counts. It has columns for 'Ratio' and 'Actual Count,' and rows for the items being compared. This grid helps you see what you know and what you need to find.
Example: The ratio of wizards to muggles is 2 to 7. There are 21 muggles. We set up the box:
| Ratio | Actual Count | |
|---|---|---|
| Wizards | 2 | ? |
| Muggles | 7 | 21 |
Section 3
Constant factor
The ratio numbers and actual counts are related by a constant factor. You can find this secret number by dividing an actual count by its corresponding ratio number. It is the key to scaling a ratio up to its real-world value.
In a ratio box, if the ratio for cats is 5 and the actual count is 20, the constant factor is 4 because .
If the ratio of goals is 3 and the team actually scored 18 goals, the constant factor is 6, since .
For a recipe with a ratio of 4 cups of flour and an actual use of 16 cups, the constant factor is .
Section 4
Solving ratio problems
To find an unknown actual count, first set up a ratio box. Second, find the constant factor using a complete row. Third, multiply the ratio number of the unknown item by the constant factor to find the final answer.
The ratio of apples to oranges is 3:4. If there are 12 apples, how many oranges? The factor is . So, oranges.
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Section 1
📘 Using a Constant Factor to Solve Ratio Problems
Ratio numbers and actual counts are related by a constant factor.
Next, you'll use a ratio box to find this constant factor and solve problems involving everything from paint mixtures to garden weeds.
Section 2
Setting up a ratio box
A ratio box organizes information by separating the numbers in a ratio from the actual counts. It has columns for 'Ratio' and 'Actual Count,' and rows for the items being compared. This grid helps you see what you know and what you need to find.
Example: The ratio of wizards to muggles is 2 to 7. There are 21 muggles. We set up the box:
| Ratio | Actual Count | |
|---|---|---|
| Wizards | 2 | ? |
| Muggles | 7 | 21 |
Section 3
Constant factor
The ratio numbers and actual counts are related by a constant factor. You can find this secret number by dividing an actual count by its corresponding ratio number. It is the key to scaling a ratio up to its real-world value.
In a ratio box, if the ratio for cats is 5 and the actual count is 20, the constant factor is 4 because .
If the ratio of goals is 3 and the team actually scored 18 goals, the constant factor is 6, since .
For a recipe with a ratio of 4 cups of flour and an actual use of 16 cups, the constant factor is .
Section 4
Solving ratio problems
To find an unknown actual count, first set up a ratio box. Second, find the constant factor using a complete row. Third, multiply the ratio number of the unknown item by the constant factor to find the final answer.
The ratio of apples to oranges is 3:4. If there are 12 apples, how many oranges? The factor is . So, oranges.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter