Fractions represent parts of a whole. Think of a pizza cut into slices. A fraction tells us how many of those slices we have compared to the total number the pizza was divided into. For example, if a pizza is cut into 4 slices and you have 3, that’s represented as the fraction 3/4.
Adding fractions is a fundamental math skill, and it’s easier than you might think! This guide breaks down the process into simple steps, making it clear and straightforward to understand.
Simple Steps to Fraction Addition
Adding fractions involves a few key steps to ensure you get the correct answer. Here’s a simple three-step process to follow:
- Step 1: Check the Denominators: Make sure the bottom numbers of the fractions (the denominators) are the same.
- Step 2: Add the Numerators: Once the denominators are the same, add the top numbers (the numerators) together. Keep the denominator the same.
- Step 3: Simplify: If possible, simplify the resulting fraction to its simplest form.
Let’s walk through some examples to see these steps in action.
Adding Fractions with the Same Denominator
This is the easiest scenario. When fractions have the same denominator, you can add them directly.
Example: 1/4 + 1/4
Step 1: The denominators are already the same (both are 4). We can skip to step 2.
Step 2: Add the numerators and keep the denominator:
1/4 + 1/4 = (1 + 1)/4 = 2/4
Step 3: Simplify the fraction. 2/4 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
2/4 = (2 ÷ 2)/(4 ÷ 2) = 1/2
So, 1/4 + 1/4 = 1/2
Visually, this looks like:
You can see how combining one quarter and another quarter results in one half. Simplifying fractions, like changing 2/4 to 1/2, gives us the simplest way to express the fraction. (Learn more about Equivalent Fractions.)
Adding Fractions with Different Denominators
What if the denominators are not the same? This is where we need to find a common denominator.
Example: 1/3 + 1/6
Step 1: The denominators are different (3 and 6). Imagine trying to add slices of different sizes – it doesn’t directly work!
We need to make the denominators the same. Notice that 6 is a multiple of 3 (6 = 3 × 2). We can convert 1/3 into an equivalent fraction with a denominator of 6. To do this, multiply both the numerator and the denominator of 1/3 by 2:
1/3 = (1 × 2)/(3 × 2) = 2/6
Remember: Multiplying both the top and bottom of a fraction by the same number doesn’t change its value.
Now our problem becomes:
2/6 + 1/6
The denominators are now the same, so we can proceed to step 2.
Step 2: Add the numerators and keep the denominator:
2/6 + 1/6 = (2 + 1)/6 = 3/6
Visually:
Step 3: Simplify the fraction. 3/6 can be simplified by dividing both the numerator and the denominator by 3:
3/6 = (3 ÷ 3)/(6 ÷ 3) = 1/2
So, 1/3 + 1/6 = 1/2
Another Example with Different Denominators
Let’s try another example where the common denominator isn’t immediately obvious.
Example: 1/3 + 1/5
Step 1: The denominators are different (3 and 5). We need to find a common denominator. A simple way to find a common denominator is to multiply the two denominators together: 3 × 5 = 15.
We need to convert both fractions to have a denominator of 15.
For 1/3, multiply the numerator and denominator by 5:
1/3 = (1 × 5)/(3 × 5) = 5/15
For 1/5, multiply the numerator and denominator by 3:
1/5 = (1 × 3)/(5 × 3) = 3/15
Now our problem becomes:
5/15 + 3/15
Step 2: Add the numerators and keep the denominator:
5/15 + 3/15 = (5 + 3)/15 = 8/15
Visually:
Step 3: Simplify the fraction. 8/15. Are there any common factors between 8 and 15? The factors of 8 are 1, 2, 4, 8. The factors of 15 are 1, 3, 5, 15. The only common factor is 1, so 8/15 is already in its simplest form.
Therefore, 1/3 + 1/5 = 8/15
Making Denominators the Same: Two Main Methods
We’ve touched on finding common denominators. Here are the two primary methods:
- Multiply the Denominators: As shown in the 1/3 + 1/5 example, multiplying the denominators always gives you a common denominator. It might not be the least common denominator, but it will work.
- Find the Least Common Multiple (LCM): The Least Common Multiple of the denominators is the smallest common denominator you can use. This often results in smaller numbers and less simplification at the end. For example, with 1/3 + 1/6, the LCM of 3 and 6 is 6, which is why we used 6 as the common denominator earlier. (Learn more about Least Common Multiple and the Least Common Denominator.)
Both methods work. Choose the one you find easier to use!
Real-World Example: Cupcake Costs
Let’s say you’re planning a cupcake business.
- You agree to give a friend 1/3 of your sales for providing ingredients.
- You also need to pay 1/4 of your sales for a market stall.
What total fraction of your sales goes to these costs?
We need to add 1/3 and 1/4.
1/3 + 1/4 = ?/?
First, make the denominators the same. Multiply the denominators: 3 × 4 = 12. So, we’ll use 12 as the common denominator.
Convert 1/3 to a fraction with denominator 12:
1/3 = (1 × 4)/(3 × 4) = 4/12
Convert 1/4 to a fraction with denominator 12:
1/4 = (1 × 3)/(4 × 3) = 3/12
Now, add the fractions:
4/12 + 3/12 = (4 + 3)/12 = 7/12
Answer: 7/12 of your cupcake sales will go towards ingredients and the market stall cost.
Adding Mixed Fractions
For more advanced fraction addition, especially with mixed fractions (like 11/2), we have a dedicated guide on Adding Mixed Fractions.
Adding fractions is a key skill in math. By following these steps and practicing, you’ll become confident in adding fractions in no time!
Introduction to Fractions
Simplifying Fractions
Equivalent Fractions
Least Common Multiple
Least Common Multiple Tool
Least Common Denominator
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
Fractions Index
