# SOLVING EQUATIONS INVOLVING FRACTIONS WORKSHEET

Solving Equations Involving Fractions Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on solving equations with fractions.

Before look at the worksheet, if you would like to know, how to solve equations with fractions,

## Solving Equations Involving Fractions Worksheet - Problems

Problem 1 :

Solve for n :

x/4 + 3  =  x/6 + 7

Problem 2 :

Solve for n :

7n/10 + 3/2  =  3n/5 + 2

Problem 3 :

Solve for k :

k/7 - 6  =  3k/7 + 4

Problem 4 :

Solve for m :

1/3 + 2m  =  m - 3/2

Problem 5 :

Solve for x :

1/2 + 2x/5 - 1  =  x/5 + x

## Solving Equations Involving Fractions Worksheet - Solutions

Problem 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.

Problem 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.

Problem 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.

Problem 4 :

Solve for m :

1/3 + 2m  =  m - 3/2

Solution :

Step 1 :

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

LCM of (3, 2)  =  6

Step 2 :

Multiply each side of the fraction by 6.

6(1/3 + 2m)  =  6(m - 3/2)

Use distributive property.

2 + 12m  =  6m - 9

Subtract 6m from each side.

2 + 6m  =  - 9

Subtract 2 from each side.

6m  =  - 11

Divide each side by 6.

m  =  -11/6

So, the value of m is -11/6.

Problem 5 :

Solve for x :

1/2 + 2x/5 - 1  =  x/5 + x

Solution :

Step 1 :

Find the least common multiple of the denominators 2, 5 and 5.

LCM of (2, 5, 5)  =  10

Step 2 :

Multiply each side of the fraction by 10.

10(1/2 + 2x/5 - 1)  =  10(x/5 + x)

Use distributive property.

5 + 4x - 10  =  2x + 10x

Simplify.

4x - 5  =  12x

Subtract 4x from each side.

- 5  =  8x

Divide each side by 8.

-5/8  =  x

So, the value of x is -5/8.

After having gone through the stuff given above, we hope that the students would have understood, how to solve equations with fractions.

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