## Algebra Rule 5

#### How to turn two fractions summed into one larger fraction

```\left({a \over b}\right)+\left({c \over d}\right) = {(ad+bc) \over bd}```

**Description:**This follows from the fact that you can find a common denominator between two fractions by multiplying the numerator and denominator of each fraction by the other's denominator, like so:

```{3 \over 5}+{1 \over 3} = {(3*3) \over (5*3)} + {(1*5) \over (3*5)} = {9 \over 15} + {5 \over 15} = {14 \over 15} ``` or, written as in the above rule: ```
{3 \over 5}+{1 \over 3} = {(3*3) \over (5*3)} + {(1*5) \over (3*5)} = {(1*5)+(3*3) \over (3*5)}```

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