Problem 4 - Prealgebra

Question

Write each percent as a fraction with denominator \(100 .\) $$80 \%$$

Step-by-Step Solution

Answer

80% as a fraction is \( \frac{4}{5} \).

Step 1: Understand Percent

The percent symbol (%) represents a ratio out of 100. So when you see \(80\%\), it means 80 out of 100.

Step 2: Write Percent as a Fraction

To convert \(80\%\) to a fraction, write it as \(\frac{80}{100}\). This directly translates the percent into a fraction, with the percent as the numerator and 100 as the denominator.

Step 3: Simplify the Fraction

Check if the fraction \(\frac{80}{100}\) can be simplified. Both 80 and 100 have a common factor of 20. Divide the numerator and the denominator by 20: \(\frac{80 \div 20}{100 \div 20} = \frac{4}{5}\).

Key Concepts

Simplifying Fractions

Fractions represent a division between two numbers, and simplifying them means reducing the fraction to its simplest form, where the numerator and denominator have no common factors apart from 1.
To simplify a fraction like \( \frac{80}{100} \), we look for the greatest common factor (GCF) of both the numerator and the denominator.
In this case, the GCF of 80 and 100 is 20. By dividing both the numerator and the denominator by this GCF, we get:

• \( \frac{80}{100} \div \frac{20}{20} = \frac{4}{5} \)

Now, \( \frac{4}{5} \) is the simplest form of the fraction. Simplifying fractions not only makes them easier to read, but also useful in comparisons. Remember, a simplified fraction still represents the same number, just in a more concise form.

Understanding Percentages

Percentages are an essential part of math that depict a number as a part of 100. The symbol '%' stands for "per hundred."
Thus, when you see \(80\%\), it translates to 80 out of 100.
This concept is often used to calculate discounts, interests, and statistics in everyday life.Whenever you encounter a percentage, you can easily convert it to a fraction by writing it over 100, effectively changing it to a form that is often easier to work with in math equations. This conversion gives a clearer picture of parts of a whole in numerous scenarios.

Fraction Basics

Fractions are a fundamental component of mathematics and are printed as \(\frac{a}{b}\), where 'a' is the numerator and 'b' is the denominator.
The numerator depicts how many parts we have, while the denominator illustrates how many equal parts the whole is divided into.
For example, \(\frac{3}{4} \) represents 3 parts out of 4 equal parts. Understanding this concept is crucial as it applies to a wide array of mathematical situations, from simple addition and subtraction of fractions to more complex operations. Fractions allow for a comprehensive representation of non-whole numbers and are frequently used in measurements, cooking, and beyond.