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Chapter 7: Problem 49

Convert each fraction or mixed number to a percent. $$\frac{3}{5}$$

Short Answer

Expert verified
\( \frac{3}{5} \) is 60\%.

Step by step solution

01

Understand the Concept

To convert a fraction to a percent, we need to multiply the fraction by 100. This is because a percent is essentially a fraction with a denominator of 100.
02

Write the Fraction

Start with the given fraction, which is \( \frac{3}{5} \).
03

Divide to get a Decimal

Perform the division \( 3 \div 5 \) to convert the fraction into a decimal. This gives \( 0.6 \).
04

Convert Decimal to Percent

Multiply the decimal \( 0.6 \) by 100 to get the percent. This gives \( 0.6 \times 100 = 60 \).
05

Write the Answer

Therefore, \( \frac{3}{5} \) as a percent is \( 60\% \).

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Key Concepts

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

Fraction to Percent
When you want to convert a fraction into a percent, think about the connection between fractions, decimals, and percents. A fraction like \( \frac{3}{5} \) represents parts of a whole, where we have 3 parts out of 5. To convert this fraction into a percent, we multiply by 100. Why? Because percent means "per hundred." Essentially, you're finding how much of those 5 parts would make up 100 parts. This method converts the fraction into a meaningful, real-world percentage.

Here are the steps you take:
  • Start with the fraction, \( \frac{3}{5} \).
  • Multiply by 100. This looks like \( \frac{3}{5} \times 100 \).
  • Calculate to find the percent: the calculation gives you 60.
Therefore, \( \frac{3}{5} \) is equivalent to 60%, meaning 60 out of every 100 parts.
Decimal Conversion
Converting a fraction to a decimal is a simple process that involves division. For the fraction \( \frac{3}{5} \), you divide the numerator (3) by the denominator (5). Think of this as finding how many times 5 fits into 3, with a decimal remainder.

Here's how:
  • Perform the division: 3 divided by 5 is 0.6.
  • This decimal, 0.6, is directly linked to the fraction \( \frac{3}{5} \).
Decimal conversion helps provide a clearer, often more practical, representation of fractions, especially when working with real-world problems. Once in decimal form, converting to other formats such as percent becomes a straightforward task.
Basic Arithmetic
Understanding basic arithmetic is key to working with fractions, decimals, and percentages. In this exercise, basic arithmetic operations include division and multiplication which are essential for converting between these forms.

Key steps involve:
  • Division: Divide the numerator by the denominator to convert a fraction into a decimal.
  • Multiplication: Multiply the resulting decimal by 100 to find its percent equivalent.
These operations reinforce how different mathematical representations can express the same value. By mastering these basic arithmetic skills, you enhance your problem-solving abilities across various mathematical contexts.

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