Percent and Fraction Lesson: Understanding Their Relationship

Lesson Overview

• What Are Fractions?
• What Are Percentages?
• Converting Between Fractions and Percentages
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions

In mathematics, fractions and percentages are two ways of expressing parts of a whole. Although they may seem different, they are closely related and can be converted into each other. 

Understanding how fractions and percentages work is essential for solving problems in everyday life, such as calculating discounts, measuring ingredients in recipes, or understanding data in surveys. In this lesson, we will explore the concepts of fractions and percentages, how to convert between them, and how to perform operations using these forms of numbers.

What Are Fractions?

A fraction represents a part of a whole. It consists of two parts:

• The numerator (top number) represents how many parts you have.
  
• The denominator (bottom number) represents the total number of equal parts in the whole.
  

For example, 1/2 means one part out of two equal parts, while 3/4 means three parts out of four equal parts.

Simplifying Fractions:

Fractions can often be simplified by dividing both the numerator and the denominator by their greatest common factor (GCF). For example:

• 6/8 can be simplified to 3/4 by dividing both numbers by 2.
  

Equivalent Fractions:

Fractions that represent the same value but have different numerators and denominators are called equivalent fractions. For example:

• 2/4, 4/8, and 1/2 are all equivalent fractions.
  

What Are Percentages?

A percentage is a way of expressing a number as a part of 100. Percentages are commonly used in many areas of life, including shopping (discounts), sports (statistics), and finance (interest rates).

• 50 percent means 50 out of 100, or 1/2.
  
• 25 percent means 25 out of 100, or 1/4.
  

Percentages are often used to express a fraction of something in a more understandable way, especially when comparing different quantities.

Converting Fractions to Percentages:

To convert a fraction to a percentage, you multiply it by 100. For example, to convert 3/4 into a percentage: 3/4 × 100 = 75 percent
So, 3/4 is equivalent to 75 percent.

Converting Decimals to Percentages:

To convert a decimal to a percentage, you multiply it by 100. For example, to convert 0.25 into a percentage: 0.25 × 100 = 25 percent
So, 0.25 is equivalent to 25 percent.

Converting Between Fractions and Percentages

Understanding how to convert between fractions and percentages is an important skill. Here's how to do it:

1. From Fraction to Percentage:

To convert a fraction to a percentage, first convert it to a decimal by dividing the numerator by the denominator. Then, multiply the decimal by 100.

• Example: Convert 2/5 to a percentage. 2/5 = 0.4 and 0.4 × 100 = 40 percent
  

2. From Percentage to Fraction:

To convert a percentage to a fraction, write the percentage as a fraction over 100 and simplify it.

• Example: Convert 75 percent to a fraction. 75% = 75/100 = 3/4
  

3. From Decimal to Percentage:

To convert a decimal into a percentage, multiply it by 100.

• Example: Convert 0.6 to a percentage. 0.6 × 100 = 60 percent
  

4. From Percentage to Fraction:

To convert a percentage to a fraction, write the percentage as a fraction over 100 and simplify.

• Example: Convert 25 percent to a fraction. 25% = 25/100 = 1/4
  

Take This Quiz:

Fractions Decimals And Percentages Quiz

Adding and Subtracting Fractions

When adding or subtracting fractions, it's essential to first make sure the fractions have the same denominator. Here's how to add and subtract fractions:

1. Adding Fractions with the Same Denominator:

When the fractions have the same denominator, simply add the numerators and keep the denominator the same.

• Example: Add 3/10 and 4/10. 3/10 + 4/10 = 7/10
  

2. Adding Fractions with Different Denominators:

When the fractions have different denominators, you need to find a common denominator. Once you have a common denominator, you can add the fractions.

• Example: Add 1/2 and 1/3. The least common denominator (LCD) of 2 and 3 is 6. Convert both fractions to have a denominator of 6: 1/2 = 3/6 and 1/3 = 2/6 Now add the fractions: 3/6 + 2/6 = 5/6
  

3. Subtracting Fractions:

Subtracting fractions follows the same rule as adding fractions. Ensure the denominators are the same, and then subtract the numerators.

• Example: Subtract 5/8 and 3/8: 5/8 - 3/8 = 2/8 = 1/4
  

Multiplying and Dividing Fractions

Multiplying and dividing fractions follows different rules from addition and subtraction. Here's how to multiply and divide fractions:

1. Multiplying Fractions:

To multiply fractions, simply multiply the numerators and multiply the denominators.

• Example: Multiply 1/2 and 3/4. 1/2 × 3/4 = 3/8
  

2. Dividing Fractions:

To divide fractions, you multiply by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and the denominator.

• Example: Divide 3/5 by 2/3. First, find the reciprocal of 2/3, which is 3/2. Now multiply: 3/5 × 3/2 = 9/10
  

Examples of Fractions and Percentages

Fractions and percentages are used in many real-world situations. Here are a few examples:

• Shopping: When there's a sale, prices are often given as percentages. For example, a 20 percent discount on an item means you pay 80 percent of the original price.
  
• Cooking: Recipes often use fractions to indicate ingredient amounts. For example, if a recipe calls for 1/4 cup of sugar, that's a fraction of the total amount.
  
• Sports: Statistics in sports are often represented as percentages. For example, a player might have a shooting percentage in basketball, which tells you how often they make a basket.
  

Take This Quiz:

Percent And Fraction: Math Test Quiz!

Practice Problems

Let's test your understanding of fractions and percentages with a few practice problems:

1. What is 3/5 + 2/5?
   
2. Convert 7/8 - 3/8 to a simplified fraction.
   
3. Multiply 4/5 × 2/3.
   
4. Divide 7/10 ÷ 3/5.
   
5. What is 25 percent as a fraction?