Find the missing numerator: [tex]$\frac{10}{15}=\frac{?}{60}$[/tex].
Answer (1)
Set up the proportion: 15 10 = 60 x .
Simplify the fraction: 15 10 = 3 2 .
Multiply both sides by 60: x = 3 2 × 60 .
Calculate the missing numerator: x = 40 . The missing numerator is 40 .
Explanation
Setting up the Proportion We are given the proportion 15 10 = 60 ? and need to find the missing numerator. Let's call the missing numerator x . So, the proportion can be written as 15 10 = 60 x .
Isolating x To solve for x , we can multiply both sides of the equation by 60: x = 15 10 × 60
Simplifying the Fraction First, let's simplify the fraction 15 10 by dividing both the numerator and the denominator by their greatest common divisor, which is 5: 15 10 = 15 ÷ 5 10 ÷ 5 = 3 2
Substituting the Simplified Fraction Now, substitute the simplified fraction back into the equation for x :
x = 3 2 × 60
Calculating x To calculate x , we can multiply the fraction by 60: x = 3 2 × 60 = 3 120 = 40
Conclusion Therefore, the missing numerator is 40.
Examples
Proportions are used in everyday life, such as when scaling recipes. If a recipe calls for 2 cups of flour for 12 cookies, you can use a proportion to find out how much flour you need for 36 cookies. Setting up the proportion 12 2 = 36 x and solving for x will tell you how many cups of flour are needed.
