Add Fractions Calculator
Enter two fractions or mixed numbers to find their sum, simplified to lowest terms, with every step shown.
Updated
Add Fractions Calculator
Our Add Fractions Calculator adds two fractions or mixed numbers and gives the sum in lowest terms. Type the numerators and denominators and the answer appears straight away as a simplified fraction, a mixed number and a decimal, with every step shown: the least common denominator, the rewritten fractions, the added numerators and the simplification. It works with negative fractions and very large numbers, always exactly.
Quick answer
To add fractions, rewrite them over a common denominator, add the numerators and simplify. For example, 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Enter any two fractions above and the calculator shows the sum instantly.
- Same denominator: add the numerators, 3/8 + 5/8 = 8/8 = 1
- Different denominators: use the least common denominator (LCD)
- Formula: a/b + c/d = (a × d + b × c) / (b × d), then simplify
- Never add the denominators: 1/2 + 1/3 is 5/6, not 2/5
How to Add Fractions
A fraction's denominator says what size the pieces are, and the numerator says how many pieces there are. You can only add pieces of the same size, so adding fractions takes three steps:
- Find a common denominator, ideally the least common denominator (LCD).
- Rewrite each fraction over it, multiplying the top and bottom by the same number.
- Add the numerators, keep the denominator, and simplify the result.
Adding Fractions With the Same Denominator
When the denominators already match, add the numerators and keep the denominator:
= 8/8 = 1
Three eighths of a pizza plus five eighths is the whole pizza.
Adding Fractions With Different Denominators
Rewrite both fractions over the least common denominator first. For 1/4 + 1/6 the LCD is 12:
1/6 = 2/12 (× 2)
3/12 + 2/12 = 5/12
The shortcut formula multiplies the denominators instead:
1/4 + 1/6 = (6 + 4)/24
= 10/24 = 5/12
It always works, but gives bigger numbers that need simplifying. The calculator uses the LCD and shows each step.
Finding the Least Common Denominator
The LCD is the least common multiple of the denominators, the smallest number they both divide into. Two quick ways to find it:
- List multiples: multiples of 10 are 10, 20, 30; multiples of 15 are 15, 30. The LCD of 10 and 15 is 30.
- Use the GCD: LCD = (b × d) ÷ GCD(b, d). For 12 and 8: 96 ÷ 4 = 24.
So 7/10 + 4/15 = 21/30 + 8/30 = 29/30, and 5/12 + 3/8 = 10/24 + 9/24 = 19/24.
Adding Mixed Numbers
Turn each mixed number into an improper fraction (whole × denominator + numerator), add, then turn the answer back. For 1 1/2 + 2 1/3:
3/2 + 7/3 = 9/6 + 14/6
= 23/6 = 3 5/6
You can also add the whole numbers and the fractions separately: 1 + 2 = 3 and 1/2 + 1/3 = 5/6, so the sum is 3 5/6. Choose Mixed in the calculator to type a whole number for each fraction.
Adding Negative Fractions
Adding a negative fraction is the same as subtracting. The rules for the common denominator do not change:
= −7/20
For a negative mixed number such as −1 1/2, the minus sign applies to the whole thing, so it is −3/2. Type the minus sign in front of the whole number.
Common Fraction Sums
| Sum | LCD | Answer |
|---|---|---|
| 1/2 + 1/4 | 4 | 3/4 |
| 1/2 + 1/3 | 6 | 5/6 |
| 1/3 + 1/6 | 6 | 1/2 |
| 2/3 + 3/4 | 12 | 17/12 = 1 5/12 |
| 5/12 + 3/8 | 24 | 19/24 |
| 7/10 + 4/15 | 30 | 29/30 |
Common Mistakes
- Adding the denominators. 1/2 + 1/3 is 5/6, not 2/5.
- Changing only the denominator. When 1/4 becomes twelfths, the numerator is multiplied too: 3/12, not 1/12.
- Forgetting to simplify. 10/24 is correct but not finished; it reduces to 5/12.
- Mixed numbers with a minus sign. −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2.
- A zero denominator. A fraction with denominator 0 is undefined.
Key Terms
- Numerator
- The top number: how many pieces.
- Denominator
- The bottom number: the size of the pieces.
- LCD
- Least common denominator, the smallest shared denominator.
- Improper
- A fraction whose numerator is at least its denominator, such as 23/6.
- Mixed number
- A whole number and a fraction, such as 3 5/6.
- Simplify
- Divide the top and bottom by their GCD.
How to Use the Add Fractions Calculator
- Choose the fraction type. Pick Simple for fractions such as 3/4 or 7/2, or Mixed to add a whole-number box for mixed numbers such as 2 3/4.
- Enter the two fractions. Type the numerator in the top box and the denominator in the bottom box of each fraction. Negative numbers work; put the minus sign on the numerator, or on the whole number of a mixed number.
- Read and copy the sum. The sum appears as you type, in lowest terms. The table shows it as a fraction, a mixed number and a decimal, with the steps: the least common denominator, the rewritten fractions, the added numerators and the simplification. Press Copy to copy it, or Clear or Esc to start again.
Example: enter 1/4 and 1/6. The sum is 5/12, with the working 1/4 + 1/6 = 3/12 + 2/12 = 5/12, the decimal ≈ 0.4166666667 = 0.41(6) and the steps LCD of 4 and 6 = 12, 3 + 2 = 5.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you add fractions?
Rewrite the fractions over a common denominator, add the numerators, keep the denominator and simplify. For example 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
How do you add fractions with different denominators?
Find the least common denominator (the least common multiple of the denominators), multiply the top and bottom of each fraction so it has that denominator, then add the numerators. For 2/3 + 3/4 the LCD is 12: 8/12 + 9/12 = 17/12 = 1 5/12.
What is the formula for adding fractions?
a/b + c/d = (a × d + b × c) / (b × d). Simplify the answer afterwards: 1/4 + 1/6 = (6 + 4)/24 = 10/24 = 5/12.
Do you add the denominators when adding fractions?
No. The denominator gives the size of the pieces, which stays the same. 1/2 + 1/3 is 3/6 + 2/6 = 5/6, not 2/5.
How do you add mixed numbers?
Turn each mixed number into an improper fraction, add, and turn the answer back into a mixed number. 1 1/2 + 2 1/3 = 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6. Or add the whole numbers and the fractions separately: 3 + 5/6.
What is 1/2 + 1/3?
1/2 + 1/3 = 3/6 + 2/6 = 5/6, or about 0.8333.
What is 2/3 + 3/4?
2/3 + 3/4 = 8/12 + 9/12 = 17/12, which is 1 5/12 as a mixed number, or about 1.4167.
How do you add negative fractions?
Use a common denominator as usual and add the signed numerators. 2/5 + (−3/4) = 8/20 + (−15/20) = −7/20. A negative mixed number such as −1 1/2 is −3/2.
Does the calculator simplify the answer?
Yes. The sum is always reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor, and the steps table shows that division.
Is the Add Fractions Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Add Fractions Calculator to add any two fractions or mixed numbers, with every step shown.