solving equations with fractions

Solving a fraction equation is very similar to solving equations involving whole numbers. The main goal is to isolate the variable (usually represented by a letter like “x”) on one side of the equation. Here are the general steps to solve a fraction equation:

1. Clear the equation of fractions (if necessary): If the equation contains fractions, you can simplify it by clearing the fractions first. To do this, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators. This will eliminate the fractions. For example, if you have the equation:23�−14=5632​x−41​=65​You can clear the fractions by multiplying both sides by 12 (the LCM of 3 and 4):

   12⋅23�−12⋅14=12⋅5612⋅32​x−12⋅41​=12⋅65​

   This simplifies to:

   $8x-3=10$

2. Simplify the equation:

3. Once you’ve cleared the fractions, simplify the equation as much as possible by combining like terms. In the example above:$8x-3=10$
4. Isolate the variable:
5. Now, your goal is to isolate the variable on one side of the equation. In this case, you can do this by adding 3 to both sides to move the constant term to the other side:$8x-3+3=10+3$This simplifies to:$8x=13$

6. 

7. Solve for the variable:

8. Finally, divide both sides by the coefficient of the variable (in this case, 8) to solve for the variable:8�8=13888x​=813​�=138x=813​

So, the solution to the equation is �=138x=813​. Always remember to check your solution by plugging it back into the original equation to ensure it satisfies the equation.

These steps should help you solve fraction equations. Keep in mind that equations can vary in complexity, and some may require additional steps or techniques, especially when dealing with more advanced algebraic equations.Get free download for english worksheets with pdf

Solving fraction equations is similar to solving equations involving integers or decimals. The key is to isolate the variable (usually represented by a letter like “x”) on one side of the equation. Here are the general steps to solve a fraction equation:

1. Clear Fractions (Optional but recommended):

2. You can start by clearing the fractions in the equation. This can make the equation easier to work with. To do this, multiply both sides of the equation by the least common multiple (LCM) of the denominators. This step is optional but often simplifies the equation and easy Solving equations with fractions Worksheets
3. Simplify: If you didn’t clear fractions in step 1, simplify the equation by simplifying the fractions as much as possible.
4. Isolate the Variable: To isolate the variable, perform operations on both sides of the equation until the variable is alone on one side.a. Addition or Subtraction: If the variable is in a term with a fraction, you can start by adding or subtracting to get rid of other terms on the same side.b. Multiplication or Division: Next, you can multiply or divide to isolate the variable completely. Remember that whatever operation you perform on one side of the equation, you must also perform on the other side to maintain equality.
5. Check Your Solution: After isolating the variable and finding a solution, it’s essential to check your answer by substituting it back into the original equation to make sure it satisfies the equation.

Here’s an example to illustrate these steps:

Example:

Solve the equation (3/4)x – 1/2 = 1/8.

Step 1 (Optional):

Clear fractions by multiplying both sides by the LCM of the denominators (8):

(8 * 3/4)x – (8 * 1/2) = (8 * 1/8)

6x – 4 = 1

Step 2: Simplify further if needed:

6x – 4 = 1

Step 3: Isolate the variable:

6x – 4 + 4 = 1 + 4

6x = 5

6x/6 = 5/6

x = 5/6

Step 4: Check your solution:

(3/4)(5/6) – 1/2 = 1/8

(15/24) – 12/24 = 3/24

(15 – 12)/24 = 3/24

3/24 = 3/24 (Both sides are equal, so the solution x = 5/6 is correct)

Remember that these are the general steps to solve fraction equations. The complexity of the equation may vary, but these principles should guide you through most fraction equation problems.