A chef uses $4 \frac{3}{4}$ cups of broth for 10 servings of soup. How much broth is used in one serving of soup? Let $x$ represent the amount of broth.
equivalent ratios: $\frac{4 \frac{3}{4}}{10}=\frac{x}{1}$
Answer (2)
Convert the mixed number to an improper fraction: 4 4 3 = 4 19 .
Set up the equation to find the amount of broth per serving: x = 10 4 19 .
Divide the fraction by 10: x = 4 19 × 10 1 .
Calculate the final amount of broth per serving: x = 40 19 . The amount of broth used in one serving of soup is 40 19 cups.
Explanation
Understanding the Problem We are given that a chef uses 4 4 3 cups of broth for 10 servings of soup. We need to find out how much broth is used in one serving of soup. Let x represent the amount of broth used in one serving.
Converting to Improper Fraction First, we need to convert the mixed number 4 4 3 to an improper fraction. To do this, we multiply the whole number 4 by the denominator 4 and add the numerator 3. This gives us 4 × 4 + 3 = 16 + 3 = 19 . So, 4 4 3 = 4 19 .
Setting up the Equation Now we know that 4 19 cups of broth are used for 10 servings. To find the amount of broth used in one serving, we need to divide the total amount of broth by the number of servings. So, we have x = 10 4 19 .
Dividing Fractions To divide a fraction by a whole number, we can rewrite the whole number as a fraction with a denominator of 1. So, we have x = 1 10 4 19 . To divide fractions, we multiply by the reciprocal of the second fraction. The reciprocal of 1 10 is 10 1 . Therefore, x = 4 19 × 10 1 .
Calculating the Amount of Broth Multiplying the fractions, we get x = 4 × 10 19 × 1 = 40 19 . So, one serving of soup uses 40 19 cups of broth.
Examples
Understanding ratios and proportions is crucial in cooking and baking. For example, if you're scaling a recipe up or down, you need to maintain the correct ratios of ingredients to ensure the dish tastes as intended. If a recipe for 4 people calls for 1 cup of flour, and you want to make it for 12 people, you'll need 3 cups of flour because the ratio of people to flour must remain constant. This ensures the recipe works well regardless of the serving size.
To find the amount of broth in one serving, convert 4 4 3 to the improper fraction 4 19 and divide by 10, giving you 40 19 cups of broth per serving.
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