How To Add Fractions Khan Academy

How to Add Fractions: A Comprehensive Guide

Adding fractions might seem daunting at first, but with a clear understanding of the underlying principles, it becomes a straightforward process. This guide will walk you through adding fractions, covering various scenarios and providing practical examples. We'll break down the process step-by-step, making it easy for everyone to master.

Understanding Fractions

Before diving into addition, let's refresh our understanding of fractions. A fraction represents a part of a whole. It's composed of two main parts:

• Numerator: The top number, indicating the number of parts you have.
• Denominator: The bottom number, indicating the total number of equal parts the whole is divided into.

For example, in the fraction 3/4 (three-quarters), 3 is the numerator and 4 is the denominator. This means you have 3 out of 4 equal parts.

Adding Fractions with the Same Denominator

Adding fractions with the same denominator is the simplest case. You simply add the numerators and keep the denominator the same.

Example: 1/5 + 2/5 = (1+2)/5 = 3/5

Steps:

1. Check the denominators: Ensure both fractions have the same denominator.
2. Add the numerators: Add the numbers on top (the numerators).
3. Keep the denominator: The denominator remains unchanged.
4. Simplify (if possible): Reduce the resulting fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Adding Fractions with Different Denominators

This is where things get slightly more complex. To add fractions with different denominators, you first need to find a common denominator. This is a number that is a multiple of both denominators. The easiest common denominator to find is the least common multiple (LCM) of the denominators.

Example: 1/3 + 1/2

1. Find the LCM: The LCM of 3 and 2 is 6.
2. Convert to equivalent fractions: Rewrite each fraction with the common denominator (6):
   • 1/3 = 2/6 (multiply both numerator and denominator by 2)
   • 1/2 = 3/6 (multiply both numerator and denominator by 3)
3. Add the numerators: 2/6 + 3/6 = (2+3)/6 = 5/6

Steps:

1. Find the least common multiple (LCM) of the denominators. You can list multiples of each denominator or use prime factorization to find the LCM.
2. Convert each fraction to an equivalent fraction with the LCM as the denominator. Remember to multiply both the numerator and the denominator by the same number.
3. Add the numerators.
4. Keep the common denominator.
5. Simplify (if possible).

Adding Mixed Numbers

Mixed numbers combine a whole number and a fraction (e.g., 2 1/2). To add mixed numbers, you can either convert them to improper fractions first or add the whole numbers and fractions separately.

Example: 2 1/3 + 1 1/2

Method 1: Convert to improper fractions

1. Convert mixed numbers to improper fractions:
   • 2 1/3 = (2*3 + 1)/3 = 7/3
   • 1 1/2 = (1*2 + 1)/2 = 3/2
2. Find the LCM: LCM of 3 and 2 is 6.
3. Convert to equivalent fractions:
   • 7/3 = 14/6
   • 3/2 = 9/6
4. Add the fractions: 14/6 + 9/6 = 23/6
5. Convert back to a mixed number (if needed): 23/6 = 3 5/6

Method 2: Add whole numbers and fractions separately

1. Add the whole numbers: 2 + 1 = 3
2. Add the fractions: 1/3 + 1/2 = 5/6 (as shown in the previous example)
3. Combine the whole number and fraction: 3 + 5/6 = 3 5/6

Choose the method that you find easier and more comfortable. Both will give you the correct answer.

Practice Makes Perfect!

Adding fractions becomes easier with practice. Work through numerous examples, gradually increasing the complexity. Don't hesitate to use online resources and calculators to check your work and identify areas where you need further clarification. Mastering fractions is crucial for success in higher-level mathematics, so take your time and enjoy the learning process!