Fractions, Decimals, and Percentages Lesson

Lesson Overview

• What Are Fractions?
• What Are Decimals?
• What Are Percentages?
• Converting Between Fractions, Decimals, and Percentages
• Common Mistakes to Avoid
• Practice Problems

In mathematics, fractions, decimals, and percentages are all ways of expressing numbers in different forms. These three concepts are interconnected, and understanding how they relate to one another is essential for solving various types of math problems. Whether you're comparing numbers, calculating discounts, or analyzing data, these concepts come up frequently in everyday life.

In this lesson, we will explore what fractions, decimals, and percentages are, how to convert between them, and how to use them in different contexts. We'll also look at real-world examples and applications to help you understand their importance.

What Are Fractions?

A fraction is a way of representing a part of a whole. It consists of two numbers: the numerator (the top number) and the denominator (the bottom number). The numerator represents how many parts we have, while the denominator represents the total number of equal parts.

For example:

• 1/2 means one part out of two equal parts.
  
• 3/4 means three parts out of four equal parts.
  

Simplifying Fractions:

A fraction 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 by dividing both numbers by 2, resulting in 3/4.

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 because they represent the same part of a whole.

What Are Decimals?

A decimal is another way to represent parts of a whole. It is based on the number system that divides things into powers of ten. Decimals are written using a decimal point (e.g., 0.5, 0.25, or 1.75).

Converting Fractions to Decimals:

To convert a fraction into a decimal, divide the numerator by the denominator. For example, to convert 1/4 into a decimal:

1÷4=0.251 \div 4 = 0.251÷4=0.25

So, 1/4 is equivalent to 0.25 as a decimal.

Decimal Places:

The numbers after the decimal point represent parts of a whole. Each place represents a power of ten:

• The first place after the decimal is tenths (1/10).
  
• The second place is hundredths (1/100).
  
• The third place is thousandths (1/1000).
  

For example, 0.75 means 75 hundredths or 75/100.

Take This Quiz:

Fractions Decimals And Percentages Quiz

What Are Percentages?

A percentage is a way of expressing a number as a part of 100. It is essentially a fraction with a denominator of 100. The percentage symbol % indicates that the number is out of 100.

For example:

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

Converting Fractions to Percentages:

To convert a fraction to a percentage, multiply it by 100. For example, to convert 3/4 into a percentage:

3/4​×100=75%

So, 3/4 is equivalent to 75%.

Converting Decimals to Percentages:

To convert a decimal into a percentage, multiply it by 100. For example, to convert 0.25 into a percentage:

0.25×100=25%

So, 0.25 is equivalent to 25%.

Converting Between Fractions, Decimals, and Percentages

Understanding how to convert between fractions, decimals, and percentages is a crucial skill in math. Here's how to convert from one form to another:

1. From Fraction to Decimal:

To convert a fraction to a decimal, divide the numerator by the denominator. For example:

• 1/2 becomes 0.5 (1 ÷ 2 = 0.5).
  

2. From Fraction to Percentage:

To convert a fraction to a percentage, first convert it to a decimal and then multiply by 100. For example:

• 3/4 becomes 0.75 (3 ÷ 4 = 0.75), and then 0.75 × 100 = 75%.
  

3. From Decimal to Fraction:

To convert a decimal to a fraction, count the number of decimal places. For example:

• 0.75 is equivalent to 75/100, which simplifies to 3/4.
  

4. From Decimal to Percentage:

To convert a decimal to a percentage, multiply by 100. For example:

• 0.25 becomes 25% (0.25 × 100 = 25%).
  

5. From Percentage to Fraction:

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

• 25% becomes 25/100, which simplifies to 1/4.
  

Take This Quiz:

Fraction, Decimal and Percentage Quiz

Common Mistakes to Avoid

While working with fractions, decimals, and percentages, it's easy to make mistakes. Here are some common ones to watch out for:

1. Confusing fractions and percentages: For example, 1/2 is 50%, but 1/3 is approximately 33.33%.
   
2. Misplacing the decimal point: When converting between decimals and percentages, always remember to multiply or divide by 100.
   
3. Not simplifying fractions: Always simplify fractions if possible. For example, 8/10 should be simplified to 4/5.
   

Practice Problems

Let's test your understanding with a few practice problems:

1. What is 3/5 as a decimal and percentage?
   
2. Convert 0.4 to a fraction and percentage.
   
3. A shirt costs $30, and there's a 25% off sale. How much will the shirt cost after the discount?
   

Take This Quiz:

Fraction, Decimal, and Percent Mini-Quiz