Find the missing number in the proportion.
[tex]$\frac{5}{2}=\frac{15}{c}$[/tex]
Answer (2)
We have the proportion 2 5 = c 15 .
Cross-multiply to get 5 c = 2 × 15 .
Simplify to 5 c = 30 .
Divide by 5 to find c = 5 30 = 6 .
Explanation
Understanding the Proportion We are given the proportion 2 5 = c 15 and we need to find the value of c that makes this proportion true. A proportion states that two ratios are equal.
Cross-Multiplication To solve for c , we can use cross-multiplication. This means we multiply the numerator of the first fraction by the denominator of the second fraction, and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction. So, we have:
5 × c = 2 × 15
Simplifying the Equation Now, we simplify the equation:
5 c = 30
Isolating c To isolate c , we divide both sides of the equation by 5:
5 5 c = 5 30
Finding the Value of c Performing the division, we get:
c = 6
Conclusion Therefore, the missing number in the proportion is 6.
Examples
Proportions are used in everyday life, such as when scaling recipes. For example, if a recipe calls for 2 cups of flour to make 5 servings, you can use a proportion to determine how much flour you need to make 15 servings. Setting up the proportion 5 2 = 15 x , you can solve for x to find the amount of flour needed. Cross-multiplication gives 5 x = 30 , so x = 6 cups of flour. This ensures the recipe maintains the correct ratio of ingredients for the desired number of servings.
By cross-multiplying in the proportion 2 5 = c 15 , we find that c = 6 . This is done by setting up the equation 5 c = 30 and solving for c . Thus, the missing number is 6.
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