Find the missing number in the proportion.
[tex]$\frac{10}{6}=\frac{100}{d}$[/tex]
Answer (1)
Set up the proportion: 6 10 = d 100 .
Cross-multiply: 10 d = 6 × 100 .
Simplify: 10 d = 600 .
Solve for d : d = 10 600 = 60 . The missing number is 60 .
Explanation
Understanding the Proportion We are given the proportion 6 10 = d 100 and we need to find the value of d . A proportion states that two ratios are equal. In this case, the ratio of 10 to 6 is equal to the ratio of 100 to d .
Cross-Multiplication To solve for d , we can use cross-multiplication. 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. So we have:
10 × d = 6 × 100
Simplifying the Equation This simplifies to:
10 d = 600
Isolating d Now, to isolate d , we divide both sides of the equation by 10:
10 10 d = 10 600
Solving for d This gives us:
d = 60
Final Answer Therefore, the missing number in the proportion is 60.
Examples
Proportions are used in everyday life, such as when scaling recipes. For example, if a recipe calls for 2 cups of flour to make 12 cookies, you can use a proportion to determine how much flour you need to make 36 cookies. Setting up the proportion as $\frac{2}{12} = \frac{x}{36}$ and solving for x, you find that you need 6 cups of flour. This ensures the recipe maintains the correct ratio of ingredients, resulting in perfectly baked cookies every time.
