Work out the value of $c$
$\frac{2}{5}=\frac{6}{c}$
Answer (1)
Cross-multiply the equation 5 2 = c 6 to get 2 c = 5 × 6 .
Simplify the equation to 2 c = 30 .
Divide both sides by 2 to isolate c : c = 2 30 .
The value of c is 15 .
Explanation
Understanding the Problem We are given the equation 5 2 = c 6 and we need to find the value of c .
Cross-Multiplication To solve for c , we can cross-multiply. 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: 2 × c = 5 × 6
Simplifying the Equation Now we simplify the equation: 2 c = 30
Solving for c To isolate c , we divide both sides of the equation by 2: c = 2 30 c = 15
Final Answer Therefore, the value of c is 15.
Examples
Imagine you are scaling a recipe. If the original recipe calls for 2 cups of flour for every 5 servings, and you want to make 6 servings, you can use this type of proportion to find out how many cups of flour you need. In this case, the equation 5 2 = c 6 helps you determine that you need 15 cups of flour for 6 servings, assuming the relationship between servings and flour is directly proportional. This concept is useful in cooking, construction, and many other fields where scaling quantities is necessary.
