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)/b`

Example:

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)/b**

**Where:**

- 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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