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# Fractions in Algebra

You can add, subtract, multiply and divide fractions in algebra in the same way that you do in simple arithmetic.

To add fractions there is a simple rule:

(You can see why this works on the Common Denominator page).

### Example:

 x + 4 + x - 3 = (x+4)(4) + (3)(x-3) = 4x+16 + 3x-9 = 7x+7 3 4 3 × 4 12 12

## Subtracting Fractions

Subtracting fractions is very similar to adding, except that the + is now -

### Example:

 x + 2 - x = (x+2)(x-2) - (x)(x) = x2-22 - x2 = -4 x x - 2 x(x-2) x2 - 2x x2 - 2x

## Multiplying Fractions

Multiplying fractions is the easiest one of all, just multiply the tops together, and the bottoms together:

### Example:

 3x × x = (3x)(x) = 3x2 = x2 x-2 3 3(x-2) 3(x-2) x-2

## Dividing Fractions

To divide fractions, first "flip" the fraction you want to divide by, then use the same method as for multiplying:

### Example:

 3y2 ÷ y = 3y2 × 2 = (3y2)(2) = 6y2 = 6y x+1 2 x+1 y (x+1)(y) (x+1)(y) x+1