4/5 as a Percentage
Answer: \( \frac{4}{5} \) as a percent is 80%.
Converting fractions to percentages is a fundamental math skill that is widely used in various aspects of daily life, including finance, education, and data analysis.
In this guide, we’ll explore the methods and reasoning behind converting the fraction 4/5 into a percentage.
What is a Percent?
A percent is a way of expressing a number as a fraction of 100. The term “percent” literally means “per hundred.” Percentages are denoted using the percent sign (%). For example, 50% means 50 out of 100.
Methods to Convert 4/5 to a Percent
There are several methods to convert a fraction to a percent. We’ll explore two common approaches:
- Fraction to Decimal to Percent
- Cross-Multiplication Method
Method 1: Fraction to Decimal to Percent
This method involves two main steps:
- Convert the fraction to a decimal.
- Convert the decimal to a percent.
Step 1: Convert the Fraction to a Decimal
To convert \( \frac{4}{5} \) to a decimal, divide the numerator (4) by the denominator (5):
\[ \frac{4}{5} = 4 \div 5 = 0.8 \]
Step 2: Convert the Decimal to a Percent
To convert the decimal 0.8 to a percent, multiply it by 100:
\[ 0.8 \times 100 = 80\% \]
Conclusion of Method 1
\[ \frac{4}{5} = 80\% \]
Method 2: Cross-Multiplication Method
This method involves setting up a proportion where the fraction is equivalent to a percent expressed as \( \frac{x}{100} \), and then solving for \( x \).
Step 1: Set Up the Proportion
\[ \frac{4}{5} = \frac{x}{100} \]
Step 2: Cross-Multiply
Multiply the numerator of the first fraction by the denominator of the second fraction and vice versa:
\[ 4 \times 100 = 5 \times x \]
\[ 400 = 5x \]
Step 3: Solve for \( x \)
Divide both sides of the equation by 5 to isolate \( x \):
\[ x = \frac{400}{5} = 80 \]
Conclusion of Method 2
\[ \frac{4}{5} = 80\% \]
Summary
Both methods yield the same result:
\[ \frac{4}{5} = 80\% \]
This means that \( \frac{4}{5} \) is equivalent to 80 percent.
Additional Tips
Remember the Basics: Always remember that “percent” means “per hundred.” This is the key concept behind all percentage calculations.
Practice with Different Fractions: Try converting other fractions to percentages using both methods to reinforce your understanding.
Use a Calculator for Complex Fractions: For fractions that don’t convert neatly, using a calculator can save time and reduce errors.
Practice Problem
Convert \( \frac{7}{8} \) to a percent using both methods discussed.
Method 1: Fraction to Decimal to Percent
\[ \frac{7}{8} = 7 \div 8 = 0.875 \]
\[ 0.875 \times 100 = 87.5\% \]
Method 2: Cross-Multiplication
\[ \frac{7}{8} = \frac{x}{100} \]
\[ 7 \times 100 = 8x \Rightarrow 700 = 8x \Rightarrow x = \frac{700}{8} = 87.5 \]
\[ \frac{7}{8} = 87.5\% \]
By practicing with various fractions, you’ll become proficient in converting any fraction to a percent effortlessly.