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Chapter 11: Problem 29

Convert \(\frac{5}{16}\) to a percent.

Short Answer

Expert verified
\( \frac{5}{16} \) is 31.25%.

Step by step solution

01

Understand Percent Conversion

To convert a fraction into a percent, you need to convert it into a corresponding fraction with 100 as the denominator, or simply multiply the fraction by 100.
02

Multiply by 100

Multiply the given fraction by 100 to transform it into a percent. Here, calculate: \( \frac{5}{16} \times 100 \).
03

Simplify the Multiplication

Perform the multiplication using fractions: \( \frac{5\times 100}{16} = \frac{500}{16} \).
04

Calculate the Division

Divide 500 by 16 to simplify the fraction and get the percentage value. \( 500 \div 16 = 31.25 \).
05

Write the Answer as a Percent

Finally, express the result from the division step as a percent: 31.25%.

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Key Concepts

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

Fraction to Percent
Converting a fraction to a percent is a common mathematical task. Percentages express a number as a part of 100. To change a fraction into a percent, follow these straightforward steps:
  • Recognize the fraction you need to convert. For example, the fraction in question is \( \frac{5}{16} \).
  • Convert the fraction by finding an equivalent fraction with a denominator of 100. This can sometimes feel tricky, so another method is simply to multiply the fraction by 100.
Multiplying the fraction by 100 essentially scales it to a percentage as this factors in parts of 100 clearly.
This method is beneficial when the denominator does not easily multiply to 100, as is the case with 16.
Multiplying Fractions
When multiplying fractions, remember this rule: multiply the numerators together and the denominators together. Here鈥檚 how you do it step by step:
  • Take the fraction \( \frac{5}{16} \).
  • To make it a percentage, multiply it by 100. It looks like: \( \frac{5}{16} \times 100 \).
The multiplication step becomes \( \frac{5 \times 100}{16} \), which results in \( \frac{500}{16} \).
This process helps break down the problem into manageable parts, making it easier to solve.
Division Calculation
The final step in converting the fraction \( \frac{5}{16} \) into a percentage involves division. This is because the numerator from the multiplication stage (500) is larger than the denominator (16), meaning a division is necessary:
  • Divide the numerator (500) by the denominator (16): \( 500 \div 16 \).
  • Performing this division will give you 31.25.
  • This value is your percentage, thus \( 31.25\% \).
Breaking it down this way helps clarify why each step is necessary. Division here is the final crucial component to finish off our percent conversion.

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Most popular questions from this chapter

Translate each phrase or sentence to a mathematical expression or equation. When seven times a number is decreased by two times the number, the result is negative one.

Translate each phrase or sentence to a mathematical expression or equation. When eight times a number is increased by five, the result is equal to the original number plus twenty-six.

For problems \(57-140\), solve each equation. $$ 3 x+2=7 $$

Translate each phrase or sentence to a mathematical expression or equation. A number increased by one.

For problems \(57-140\), solve each equation. $$ \frac{3 z}{4}=\frac{-7}{8} $$
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