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Fractions-DECODED!

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Reciprocal

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Simplifying Fractions IV

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Prime Numbers

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Adding Fractions

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Add the two fractions.

Two fractions are added by expanding them to the common denominator and then adding their numerators.

Check whether the result can be simplified.

If you would like to have a vivid explanation with a detailed example, please read the page Addition Fraction plus Fraction - Pizza Roma with lots of cheese, please!

**Step 1: Determine the common denominator:**

The common denominator is equal to the lowest common multiple (LCM) of the two denominators: **12** (open here)

1) In order to calculate the least common multiple (LCM) of 3 and 4, you need the greatest common divisor (GCD) first:

3 ÷ 4 = 0 Remainder 3

4 ÷ 3 = 1 Remainder 1

3 ÷ 1 = 3 Remainder 0

The Greatest Common Divisor (GCD) of 3 and 4 is **1**.

2) The least common multiple (LCM) is calculated by multiplying the two numbers and then dividing by the greatest common divisor (GCD). It's easier if you first divide and then multiply:

3 × (4 : 1) = 3 × 4 = 12

**Step 2: Expand to the common denominator:**

Expand the first fraction with the number 4 and the second fraction with the number 3.

2 | + | 3 | = | 2 × 4 | + | 3 × 3 | = | 8 | + | 9 |

3 | 4 | 3 × 4 | 4 × 3 | 12 | 12 |

**Step 3: Add the numerators:**

Since the two fractions have a common denominator, you can add:

8 | + | 9 | = | 8 + 9 | = | 17 |

12 | 12 | 12 | 12 |

**Step 4: Check whether the result can be simplified**

The result can not be simplified.