# SOLVING EQUATIONS WITH FRACTIONS

The following steps will be useful to solve equations with fractions.

Step 1 :

Find the least common multiple of denominators of all the fractions found in the given equation.

Step 2 :

Multiply both sides of the equation by the least common multiple found in step 1.

Step 3 :

Now, solve for the variable.

## Solved Examples

Example 1 :

Solve for n :

x/4 + 3  =  x/6 + 7

Solution :

Step 1 :

Find the least common multiple of the denominators 4 and 6.

LCM of (4, 6)  =  12

Step 2 :

Multiply each side of the fraction by 12.

12(x/4 + 3)  =  12(x/6 + 7)

Use distributive property.

3x + 36  =  2x + 84

Subtract 2x from each side.

x + 36  =  84

Subtract 36 from each side.

x  =  48

So, the value of x is 48.

Example 2 :

Solve for n :

7n/10 + 3/2  =  3n/5 + 2

Solution :

Step 1 :

Find the least common multiple of the denominators 10, 2 and 5. LCM of (10, 2, 5)  =  5  2  1  1  1

LCM (10, 2, 5)  =  10

Step 2 :

Multiply both sides of the equation by 10.

10(7n/10 + 3/2)  =  10(3n/5 + 2)

Use distributive property.

7n + 15  =  6n + 20

Step 3 :

7n + 15  =  6n + 20

Subtract 6n from each side.

n + 15  =  20

Subtract 15 from each side.

n  =  5

So, the value of n is 5.

Example 3 :

Solve for k :

k/7 - 6  =  3k/7 + 4

Solution :

Here, we find only one denominator. That is 7.

So, multiply each side of the equation by 7.

7(k/7 - 6)  =  7(3k/7 + 4)

k - 42  =  3k + 28

Subtract k from each side.

- 42  =  2k + 28

Subtract 28 from each side.

- 70  =  2k

Divide each side by 2.

- 35  =  k

So, the value of k is -35.

Example 4 :

Solve for x :

4x/5 - 7/4  =  x/5 + x/4

Solution :

The least common multiple of the denominators (4 and 5) is 20.

Multiply each side of the equation by 20.

20[4x/5 - 7/4]  =  20[x/5 + x/4]

Use the distributive property.

20(4x/5) - 20(7/4)  =  20(x/5) + 20(x/4)

Simplify.

4(4x) - 5(7)  =  4(x) + 5(x)

16x - 35  =  4x + 5x

16x - 35  =  9x

Subtract 9x from each side.

7x - 35  =  0

7x  =  35

Divide each side by 7.

x  =  5 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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