# Solving Equations with Fractions

Fractions are just a way to represent division. We can add, subtract, multiply, and divide fractions, similar to whole numbers.

Note: When working with equations involving fractions, make sure to keep the denominators in check as they can affect your calculations.

## One-Step Equations with Fractions

In one-step equations with fractions, you’re only a step away from finding the value of the variable. For example, if you have , you can multiply both sides by 2 to get .

The main aim here is to get the variable alone on one side of the equation, and in one-step equations with fractions, this usually means getting rid of the denominator.

## Two or More step Equations with Fractions

Sometimes it takes two steps to isolate the variable. For example, consider • Step 1: Eliminate the constant term by subtracting 1 from both sides, which gives you • Step 2: Multiply both sides by 3 to get • Step 3: Then, divide both sides by 2 and you get ## Clearing the Fractions

If your equation has fractions, you can get rid of them to make the equation easier to work with. For example: A quick way to get rid of the fractions is to multiply everything in the equation by a number that turns all the fractions into whole numbers. In this case, 4 will work. So, .

After doing the multiplication, you’ll get Remember: ## Equations with Fractions on Both Sides

Sometimes you’ll find equations that have fractions on both sides. For example, let’s solve: • Multiply Everything by the Same Number: Here, 4 will also work. So, • The Fraction is Eliminated: After multiplying, you’ll have Next, isolate on one side of the equation by subtracting from both sides:  ## Practice Questions

Question 1:

Solve Multiply both sides by 3 to get Question 2:

Solve First subtract 1 from both sides to get Then multiply both sides by 4 and divide by 2 to get Question 3:

Solve Multiply every term by 6 to get Solve for x to get Question 4:

Solve Expand the brackets to get Multiply every term by 3 to clear the fraction, resulting in Solve for x to get 