Solve the proportion for the missing number.
[tex]\frac{13}{2}=\frac{}{12}[/tex]
Answer (2)
To find the missing number in the proportion 2 13 = 12 x , we can cross-multiply, which gives us the equation 156 = 2 x . Solving for x results in x = 78 , so the missing number is 78.
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Set up the proportion equation: 2 13 = 12 x .
Multiply both sides by 12 to isolate x : x = 2 13 × 12 .
Simplify the expression: x = 13 × 6 .
Calculate the final value: 78 .
Explanation
Understanding the Problem We are given the proportion 2 13 = 12 x , and our goal is to find the value of x . This is a classic problem of solving a proportion, which can be thought of as finding an equivalent fraction.
Isolating x To solve for x , we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 12: 2 13 × 12 = 12 x × 12
Simplifying the Equation Now, let's simplify the equation. On the left side, we have 2 13 × 12 . We can simplify this by first dividing 12 by 2, which gives us 6. Then, we multiply 13 by 6: 13 × 6 = 78 On the right side, the 12s cancel out, leaving us with just x : x = 78
Finding the missing number Therefore, the missing number in the proportion is 78.
Examples
Proportions are incredibly useful in everyday life. For example, if you're baking a cake and the recipe calls for 2 cups of flour for every 1 cup of sugar, and you want to make a larger cake using 6 cups of flour, you can use a proportion to find out how much sugar you need. Setting up the proportion 1 2 = x 6 , you can solve for x to find that you need 3 cups of sugar. This ensures that your cake turns out just right, maintaining the correct ratio of ingredients even when scaling the recipe up or down. Proportions are also used in map reading, scaling models, and calculating discounts.
