This adding fractions calculator is a specialized tool to simplify the process of adding two or more fractions together. This calculator automates the steps involved in fraction addition, providing quick and accurate results.
a/b + c/b = (a + c)/bExample:
1/7 + 3/7 = (1 + 3)/7 = 4/7
Adding Fractions Calculator
| Fractions | Calculation | Result |
|---|---|---|
| 1/2 + 1/3 | (1 3 + 1 2) / (2 * 3) = (3 + 2) / 6 = 5/6 | 5/6 |
| 2/5 + 1/4 | (2 4 + 1 5) / (5 * 4) = (8 + 5) / 20 = 13/20 | 13/20 |
| 3/8 + 1/2 | (3 + 4) / 8 = 7/8 | 7/8 |
| 5/12 + 1/3 | (5 + 4) / 12 = 9/12 = 3/4 | 3/4 |
| 7/10 + 1/5 | (7 + 2) / 10 = 9/10 | 9/10 |
| 1/6 + 1/2 | (1 3 + 1 1) / (6 * 3) = (3 + 1) / 6 = 4/6 = 2/3 | 2/3 |
| 3/4 + 2/3 | (3 3 + 2 4) / (4 * 3) = (9 + 8) / 12 = 17/12 | 17/12 (or 1 5/12) |
| 5/8 + 1/4 | (5 + 2) / 8 = 7/8 | 7/8 |
| 1/3 + 1/6 | (1 2 + 1 1) / (3 * 2) = (2 + 1) / 6 = 3/6 = 1/2 | 1/2 |
| 4/5 + 1/10 | (4 2 + 1 1) / (5 * 2) = (8 + 1) / 10 = 9/10 | 9/10 |
| 7/8 + 1/4 | (7 + 2) / 8 = 9/8 = 1 1/8 | 9/8 (or 1 1/8) |
| 9/10 + 1/5 | (9 + 2) / 10 = 11/10 = 1 1/10 | 11/10 (or 1 1/10) |
| 2/3 + 1/9 | (2 3 + 1 1) / (3 * 3) = (6 + 1) / 9 = 7/9 | 7/9 |
| 1/2 + 1/8 | (1 4 + 1 1) / (2 * 4) = (4 + 1) / 8 = 5/8 | 5/8 |
| 3/5 + 2/15 | (3 3 + 2 1) / (5 * 3) = (9 + 2) / 15 = 11/15 | 11/15 |
Adding Fractions Formula
Here is the formula for adding fractions with the same denominator:
a/b + c/b = (a + c)/bWhere:
- a and c are the numerators of the fractions
- b is the common denominator
To add fractions with different denominators:
- Find the least common multiple (LCM) of the denominators
- Convert each fraction to an equivalent fraction with the LCM as the denominator
- Add the numerators of the equivalent fractions
- Write the result over the LCM
For example, to add 1/3 + 2/5:
The LCM of 3 and 5 is 15
1/3 = 5/15 and 2/5 = 6/15
5/15 + 6/15 = 11/15
The final answer is 11/15
How to Calculate Addition of Fractions?
- Identify the denominators: Determine if the fractions have the same or different denominators.
- Find a common denominator (if necessary): If the denominators are different, find the least common multiple (LCM) of the denominators.
- Convert fractions: If you found a common denominator, convert each fraction to an equivalent fraction with this new denominator.
- Add the numerators: With all fractions now having the same denominator, add the numerators together.
- Simplify the result: If possible, reduce the resulting fraction to its simplest form.
Add 2/5 and 1/3.
- The denominators are different (5 and 3).
- The LCM of 5 and 3 is 15.
- Convert the fractions:
- 2/5 = (2 3)/(5 3) = 6/15
- 1/3 = (1 5)/(3 5) = 5/15
- Add the numerators: 6/15 + 5/15 = 11/15.
- The result 11/15 is already in its simplest form.
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