Constant factor
The constant factor is the multiplier that connects a simplified ratio to actual quantities in real-world situations. In Grade 6 Saxon Math Course 1, students calculate it as: Actual Count ÷ Ratio Number = Constant Factor. In a drama club where actors to stage crew is 5:2 and there are 35 actors, the constant factor is 35 ÷ 5 = 7, so stage crew = 2 × 7 = 14. Once found, the constant factor scales every part of the ratio simultaneously.
Key Concepts
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.
$$ \text{Actual Count} \div \text{Ratio Number} = \text{Constant Factor} $$.
In a ratio box, if the ratio for cats is 5 and the actual count is 20, the constant factor is 4 because $20 ÷ 5 = 4$. If the ratio of goals is 3 and the team actually scored 18 goals, the constant factor is 6, since $18 ÷ 3 = 6$. For a recipe with a ratio of 4 cups of flour and an actual use of 16 cups, the constant factor is $16 ÷ 4 = 4$.
Common Questions
What formula defines the constant factor?
Actual Count ÷ Ratio Number = Constant Factor.
Actors to crew ratio is 5:2 with 35 actors. How many crew members?
Constant factor = 35 ÷ 5 = 7. Crew = 2 × 7 = 14.
Can you use the constant factor with any part of the ratio?
Yes. Divide any known actual count by its ratio number to find the factor, then multiply all other ratio parts by that same factor.
Ratio of red to blue tiles is 3:7. If there are 42 blue tiles, how many red?
Constant factor = 42 ÷ 7 = 6. Red = 3 × 6 = 18.
Why is the factor called 'constant'?
Because it is the same number for every part of the ratio — all parts are scaled by the same multiplier.