Fill in the box $\frac{3}{8}=\frac{\square}{48}$ to make the proportion true.
Answer (1)
Set up the proportion as an equation: 8 3 = 48 x .
Multiply both sides by 48 to isolate x : x = 8 3 × 48 .
Simplify the expression: x = 3 × 6 = 18 .
The number that makes the proportion true is 18 .
Explanation
Understanding the Problem We are given the proportion 8 3 = 48 □ and we need to find the number that goes in the box to make the proportion true. Let's call the unknown number x .
Setting up the Equation We can rewrite the proportion as an equation: 8 3 = 48 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 48: 8 3 × 48 = 48 x × 48
Solving for x Now, we simplify the equation: 8 3 × 48 = x To calculate 8 3 × 48 , we can first divide 48 by 8, which gives us 6. Then, we multiply 3 by 6: 8 48 = 6 3 × 6 = 18 So, we have: x = 18
Checking the Answer Therefore, the number that goes in the box to make the proportion true is 18. We can check our answer by substituting 18 for x in the original proportion: 8 3 = 48 18 To verify, we can simplify the fraction 48 18 by dividing both the numerator and the denominator by their greatest common divisor, which is 6: 48 ÷ 6 18 ÷ 6 = 8 3 Since 48 18 simplifies to 8 3 , our answer is correct.
Final Answer The number that makes the proportion true is 18.
Examples
Proportions are used in everyday life, such as when scaling a recipe. For example, if a recipe calls for 2 cups of flour to make 12 cookies, and you want to make 36 cookies, you can use a proportion to determine how much flour you need. 12 cookies 2 cups = 36 cookies x cups . Solving for x gives x = 6 cups of flour. Understanding proportions helps in many practical situations where quantities need to be scaled up or down while maintaining the same ratio.
