Adding fractions is easier than you think! Below, you’ll find clear explanations, examples, and a calculator to help you practice and master your skills.
Result
The Basics
Find a common denominator, add the numerators, and simplify the result—that’s the secret to adding fractions!
Real-Life Uses
From cooking to DIY projects and budgeting, adding fractions is more useful than you might expect!
How to Add Common Fractions
Adding fractions is based on a simple rule: the denominators must be the same before you can add the numerators.
When denominators are the same:
\(\large \frac{1}{4} + \frac{3}{4} = \frac{1 + 3}{4} = \frac{4}{4} = 1 \)
Just add the numerators (top numbers) while keeping the denominator (bottom number) unchanged.
When denominators are different:
You need to find a common denominator:
\( \large \frac{1}{3} + \frac{1}{2} \)
- Find the LCM (least common multiple) of 3 and 2 = 6
- Convert the fractions: \( \large \frac{1}{3} = \frac{2}{6} \) and \( \large \frac{1}{2} = \frac{3}{6} \)
- Add the numerators: \( \large \frac{2}{6} + \frac{3}{6} = \frac{5}{6} \)
Formula for adding fractions with different denominators:
\(\huge \frac{a}{b} + \frac{c}{d} = \frac{a \times d + c \times b}{b \times d} \)
Always simplify your result! For example, \( \large \frac{4}{8} \) can be reduced to \( \large \frac{1}{2} \).
Why a Common Denominator Matters
A common denominator lets you compare fractions of different sizes—think of it like converting currencies to the same unit.
Without it, you can’t tell if \( \large \frac{1}{3} \) is larger or smaller than \( \large \frac{1}{4} \).
Imagine two pizzas, one cut into 3 slices, the other into 4. Which slice is bigger?
A common denominator (12) shows \( \large \frac{1}{3} = \frac{4}{12} \) and \( \large \frac{1}{4} = \frac{3}{12} \), so \( \large \frac{1}{3} \) is larger.
5 Simple Steps to Add Fractions
Check the denominators—if they’re the same, skip to step 4
Find a common denominator—usually the LCM of the denominators
Convert the fractions to the common denominator
Add the numerators while keeping the common denominator
Simplify the result to its simplest form
Practical Examples
Examples of Adding Fractions
Example 1: Fractions with the same denominator
Since the denominators are the same, just add the numerators.
Example 2: Fractions with different denominators
- LCM of 4 and 3 = 12
- \( \large \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \)
- \( \large \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
- \( \large \frac{9}{12} + \frac{8}{12} = \frac{17}{12} = 1\frac{5}{12} \)
Example 3: Whole number and fraction
Combine the whole number with the fraction to form a mixed number.
Common Mistakes to Avoid
Don’t add the denominators!
Wrong: \( \large \frac{1}{2} + \frac{1}{3} = \frac{2}{5} \) ❌
Right: \( \large \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \) ✓
No common denominator
Always convert fractions to a common denominator before adding.
Not simplifying the result
A fraction like \( \large \frac{6}{8} \) should be simplified to \( \large \frac{3}{4} \).
Not converting to a mixed number
An improper fraction like \( \large \frac{7}{4} \) is better shown as \( 1\frac{3}{4} \).
Ignoring signs
Pay attention to positive and negative signs when adding fractions.
Adding Fractions in Everyday Life
In the Kitchen
Adding \( \large \frac{1}{4} \) cup of flour to \( \large \frac{3}{4} \) cup gives you 1 cup total.
In DIY Projects
Adding \( 1\frac{1}{2} \) meters and \( \large \frac{3}{4} \) meter gives \( 2\frac{1}{4} \) meters of material.
In Budgeting
\( \large \frac{1}{4} \) of the budget plus \( \large \frac{1}{3} \) equals \( \large \frac{7}{12} \) of the total budget.
Key Takeaways
- For fractions with the same denominator, just add the numerators
- For different denominators, find a common one (use the LCM)
- Always simplify your results to the lowest terms
- Convert improper fractions to mixed numbers when needed
Practice with our calculator to sharpen your fraction-adding skills!
Back to the Calculator