# Pre-Algebra : One-Step Equations with Fractions

## Example Questions

### Example Question #1 : One Step Equations With Fractions

Solve for :

Explanation:

Isolate the variable to one side.

Multiply each side by :

Simplify and reduce:

### Example Question #2 : One Step Equations With Fractions

Solve for :

Explanation:

Step 1: Multiply both sides of the equation by the fraction's reciprocal to get alone on one side:

Step 2: Multiply:

### Example Question #3 : One Step Equations With Fractions

Solve for :

Explanation:

The goal is to isolate the variable on one side.

The opposite operation of division is multiplication, therefore , multiply each side by :

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

The identity law of multiplication takes effect and we get the solution as:

### Example Question #4 : One Step Equations With Fractions

Solve for :

Explanation:

The goal is to isolate the variable on one side.

The opposite operation of multiplication is division, therefore, we can either divide each side by  or multiply each side by its reciprocal :

The left hand side can be reduced by recalling that anything multiplying a fraction by its reciprocal is equal to 1:

The identity law of multiplication takes effect and we get the solution as:

However, this solution can be reduced by dividing both the numerator and denominator by 3:

### Example Question #4 : One Step Equations With Fractions

Solve for :

Explanation:

The goal is to isolate the variable on one side.

The opposite operation of addition is subtraction so subtract  from each side:

In order to complete the subtraction on the right hand side, we must first determine the common denominator, or common multiples of 3 and 6. The least common multiple of 3 and 6 is 6 itself.

Simplifying, we get the final solution:

### Example Question #2 : One Step Equations With Fractions

Solve for :

Explanation:

The goal is to isolate the variable on one side.

The opposite operation of subtraction is addition so add  to each side:

In order to complete the addition on the right hand side, we must first determine the common denominator, or common multiples of 6 and 12. The least common multiple of 6 and 12 is 12 itself.

Simplifying, we obtain the solution:

Reducing the fraction to its simplest terms we get the final solution:

### Example Question #1 : One Step Equations With Fractions

Solve for y

Explanation:

To get y by itself, you must divide by 6 on both sides

which simplifies to

### Example Question #6 : One Step Equations With Fractions

Solve for x

Explanation:

To get x by itself, you must multiply both sides of the equation by 5

which simplifies to

### Example Question #3 : One Step Equations With Fractions

Solve the equation below for x:

Explanation:

For this equation, isolate the variable  by preforming equivalent operations on both sides of the equation.

To isolate a variable multiplied by a fraction, any fraction multiplied by it's reciprocal equals one.

Because , we isolate , and the equation becomes

multiplying the values on the right side gives us

Solve for n: