$\frac{2}{11}=\frac{12}{x}$, then $x$ equals
Answer (2)
Cross-multiply the proportion: 2 ⋅ x = 11 ⋅ 12 .
Simplify the equation: 2 x = 132 .
Divide both sides by 2: x = 2 132 .
Find the value of x : x = 66 .
Explanation
Understanding the Problem We are given the equation 11 2 = x 12 and our goal is to find the value of x . This is a proportion problem, where two ratios are equal. To solve for x , we can use cross-multiplication.
Cross-Multiplication To solve the proportion 11 2 = x 12 , we 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 ⋅ x = 11 ⋅ 12
Simplifying the Equation Now we have the equation 2 x = 11 ⋅ 12 . We can simplify the right side of the equation by multiplying 11 and 12:
2 x = 132
Isolating x To isolate x , we divide both sides of the equation by 2:
x = 2 132
Finding the Value of x Finally, we simplify the fraction to find the value of x :
x = 66
Examples
Proportions are used in everyday life, such as when scaling a recipe. If a recipe calls for 2 cups of flour to make 12 cookies, and you want to make 66 cookies, you can use a proportion to determine how much flour you need. Setting up the proportion 12 2 = 66 x , you can solve for x to find the amount of flour needed. This ensures that the ratio of flour to cookies remains consistent, resulting in perfectly baked cookies every time.
The value of x in the equation 11 2 = x 12 is found to be 66 by using cross-multiplication. First, we cross-multiply to get 2 x = 132 , and then we divide both sides by 2 to isolate x . The final result is x = 66 .
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