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Chapter 6: Problem 9

Write a proportion for each statement. 4 is to 16 as 5 is to 20

Short Answer

Expert verified
\( \frac{4}{16} = \frac{5}{20} \)

Step by step solution

01

- Identify the terms

Determine the given terms in the statement. Here, we have 4, 16, 5, and 20.
02

- Set up the proportion

Write the terms as a proportion in the form of a fraction: \( \frac{4}{16} = \frac{5}{20} \).
03

- Simplify the fractions

Simplify each fraction to verify that they are equivalent. \( \frac{4}{16} = \frac{1}{4} \) and \( \frac{5}{20} = \frac{1}{4} \). Since both fractions are equal, the proportion is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fractions
A fraction represents a part of a whole. It consists of two parts: the numerator and the denominator. The numerator is the top number, indicating how many parts you have. The denominator is the bottom number, showing the total number of equal parts the whole is divided into. For example, in the fraction \( \frac{3}{4} \), 3 is the numerator and 4 is the denominator. This means you have 3 out of 4 equal parts. In our original exercise, we use fractions to set up a proportion: \( \frac{4}{16} = \frac{5}{20} \). This proportion tells us that the relationship between 4 and 16 is the same as the relationship between 5 and 20.
Equivalent Fractions
Equivalent fractions are different fractions that represent the same value or proportion. You can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number. For example, \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \) because if you multiply both the numerator and the denominator of \( \frac{1}{2} \) by 2, you get \( \frac{2}{4} \). In our exercise, we have the fractions \( \frac{4}{16} \) and \( \frac{5}{20} \). By simplifying them, both reduce to \( \frac{1}{4} \), which proves that they are equivalent.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form, where the numerator and denominator have no common factors other than 1. You do this by dividing both by their greatest common divisor (GCD). For instance, for the fraction \( \frac{4}{16} \), the GCD of 4 and 16 is 4. So, \( \frac{4}{16} \) simplified is \( \frac{1}{4} \). Similarly, for \( \frac{5}{20} \), the GCD of 5 and 20 is 5. So, \( \frac{5}{20} \) simplified is \( \frac{1}{4} \). This was a critical step in our exercise to show that the proportions \( \frac{4}{16} \) and \( \frac{5}{20} \) are indeed equal.

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Most popular questions from this chapter

Evelyn won an election by a ratio of 6 to \(5 .\) If she received 7230 votes, how many votes did her opponent receive?

Suppose two adults produce 63.4 lb of garbage in one week. At this rate, how many pounds will 50 adults produce in one week?

To measure the height of the Washington Monument, a student \(5.5 \mathrm{ft}\) tall measures his shadow to be \(3.25 \mathrm{ft}\). At the same time of day, he measured the shadow of the Washington Monument to be \(328 \mathrm{ft}\) long. Estimate the height of the monument to the nearest foot.

Write a proportion for each statement. Then solve for the variable. The numbers \(-3.125\) and 5 are proportional to the numbers \(-18.75\) and \(k .\)

Solve the proportions. $$\frac{x-3}{3 x}=\frac{2}{3}$$
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