Basics of Fractions

Introduction

Have you ever shared a pizza with friends, and instead of cutting it into one whole piece, you cut it into equal slices? Fractions help us describe parts of a whole. Understanding fractions is essential because they appear everywhere in life – from recipes to measurements to splitting up tasks.

Contents

• What Are Fractions?
• How to Read Fractions
• Types of Fractions
  • Addition and Subtraction of Fractions
• YouTube Video: Basics of Fractions
• Practice Questions
• Key Takeaways

What Are Fractions?

A fraction consists of two parts: the numerator (top number) and the denominator (bottom number). The numerator tells you how many parts you have, and the denominator tells you how many equal parts make up the whole.

Example:

If you have a pizza divided into 8 equal slices, and you’ve eaten 3, the fraction representing the slices you’ve eaten is:

Here:

• 3 is the numerator (slices eaten).
• 8 is the denominator (total slices).

How to Read Fractions

To read fractions:

• The numerator tells you how many parts you have.
• The denominator tells you the size of each part.

Here are some examples:

• is read as “one-half.”
• is read as “three-fourths.”
• is read as “five-eighths.”

Types of Fractions

Fractions come in different types:

1. Proper Fractions: The numerator is smaller than the denominator, e.g., or .
2. Improper Fractions: The numerator is larger than or equal to the denominator, e.g., or .
3. Mixed Numbers: A whole number combined with a fraction, e.g., or .

Reminder: You can convert an improper fraction to a mixed number by dividing the numerator by the denominator.

Addition and Subtraction of Fractions

Step 1: Identifying the Denominators

When adding or subtracting fractions, the first step is to identify the denominators of the fractions.
The denominator is the number at the bottom of the fraction.

For example, in the fraction , the denominator is 4, and in the fraction , the denominator is 5.

Step 2: Finding a Common Denominator

For fractions to be added or subtracted, they must have the same denominator.
If the denominators are not the same, you must find a common denominator.

The most common method is to find the least common denominator (LCD), which is the least common multiple (LCM) of the two denominators.

For example, for and , we find the LCM of 4 and 5.

The multiples of 4 are:
4, 8, 12, 16, 20, ...
The multiples of 5 are:
5, 10, 15, 20, 25, ...

The smallest common multiple is 20, so 20 is the least common denominator.

Step 3: Adjusting the Fractions to Have the Same Denominator

Once you have the common denominator, you adjust each fraction so that both have this denominator.
To do this, multiply both the numerator and denominator of each fraction by the necessary factor that makes the denominator equal to the common denominator.

For , multiply both the numerator and denominator by 5 to get:

For , multiply both the numerator and denominator by 4 to get:

Now, both fractions have the same denominator of 20, and they are and .

Step 4: Adding or Subtracting the Fractions

With both fractions now having the same denominator, you can add or subtract the numerators directly.

Addition Example

To add and , simply add the numerators:

Subtraction Example

To subtract from , subtract the numerators:

Step 5: Simplifying the Result

If the result can be simplified (i.e., if the numerator and denominator share any common factors), divide both by their greatest common divisor (GCD).

For example:

is already in its simplest form because 23 and 20 have no common factors other than 1.

Similarly, cannot be simplified further because 7 and 20 share no common factors.

Summary of Steps

1. Identify the denominators of the fractions.
2. Find the least common denominator (LCD) by finding the LCM of the denominators.
3. Adjust the fractions by multiplying the numerator and denominator by the factors that make the denominators equal.
4. Add or subtract the numerators while keeping the common denominator.
5. Simplify the result, if possible.

This process ensures that fractions are properly added or subtracted when their denominators differ.

YouTube Video: Basics of Fractions

Watch this video to get a more visual and detailed explanation of fractions, including how to add and subtract them with step-by-step examples.

Practice Questions

Key Takeaways

• Fractions describe parts of a whole.
• Proper fractions have smaller numerators than denominators.
• Improper fractions have numerators equal to or larger than denominators.
• Mixed numbers combine whole numbers and fractions.
• Adding and subtracting fractions requires finding common denominators.
• Mixed numbers are best handled by converting to improper fractions, adding/subtracting, and converting back.