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