Solve the proportion.
$\frac{2}{10}=\frac{11}{x}$
Answer (1)
We have the proportion 10 2 = x 11 .
Cross-multiply to get 2 x = 10 × 11 .
Simplify to 2 x = 110 .
Divide by 2 to find x = 55 .
Explanation
Understanding the Problem We are given the proportion 10 2 = x 11 . Our goal is to find the value of x that makes this proportion true. To do this, we'll use the method of cross-multiplication.
Cross-Multiplication Cross-multiplication involves multiplying the numerator of the first fraction by the denominator of the second fraction, and setting that equal to the product of the denominator of the first fraction and the numerator of the second fraction. In other words, we multiply diagonally. This gives us: 2 ⋅ x = 10 ⋅ 11 .
Simplifying the Equation Now we simplify the equation: 2 x = 110 .
Solving for x To isolate x , we divide both sides of the equation by 2: 2 2 x = 2 110 . This simplifies to x = 55 .
Final Answer Therefore, the solution to the proportion is x = 55 .
Examples
Proportions are incredibly useful in everyday life. For instance, if you're baking a cake and the recipe calls for 2 cups of flour for every 1 cup of sugar, you're using a proportion. If you want to make a larger cake and use 4 cups of flour, you can use a proportion to figure out that you'll need 2 cups of sugar. This same concept applies to scaling recipes, calculating distances on maps, and understanding ratios in science experiments. Understanding proportions helps ensure accuracy and consistency in various tasks.
