These worksheets will teach your students how to solve for variables by balancing algebraic equations.

The goal of this section is to help you master addition and subtraction that is contained within equations. The topics covered in this worksheet section include: balancing additive and subtractive algebraic equations in order to solve for a variable. Positive and negative numbers and fractions are covered. This set of worksheets introduces your students to the concept, and provides examples, short practice sets, longer sets of questions, and quizzes. Some of the equations you come across here will involve fractions and even irrational numbers at first look. Just take your time and look at each equation thoroughly, you might see something you didn't after the first glance. These worksheets demonstrate how to solve linear equations with and without fractions and provide practice equations for each method.

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Print Addition and Subtraction Equation Worksheets

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Solving Addition Equation Lesson

Solving Addition Equation Lesson

Learn how to solve the following equation that includes fractions: y + 2/10 = 2/10. We will walk you through how to handle all the necessary operations.

Addition and Subtraction to Solve Equations Worksheet

Addition and Subtraction to Solve Equations

You will be given a lesson that demonstrates how to solve these problems and then you are asked to solve an equation with fractions. The answer may be a negative fraction. Example: 1/12 - y = 5/6

Practice Worksheet

Practice Worksheet

Solve these 10 equations. Example: 5/11 + y = 52/6. Remember that you can check your answer by putting it in place of the variable and see if it works out.

Unconventional Worksheet

Unconventional Worksheet

Follow the process that we explained above to track your way through these problems. Example: 210/x = 8. The second part of this worksheet will have you solve the problem without all the complex math.

Solving Equations with Fractions Worksheet

Solving Equations with Fractions

8 problems can be found on this worksheet. The problems are a bit more complex. Example: 3/11 - x = 6/12

Wrap Up Worksheet

Wrap Up Worksheet

Solve these equations with fractions. Example: What is the perimeter of a rectangle whose longer side is 102/6 and the shorter side is half of that?

Different Signs Lesson

Different Signs Lesson

Learn how to solve linear equations such as the following: -x = 8 - 14. It will show you how to handle integers that have the same or different signs when solving these problems.

Working Math Statements Worksheet

Working Math Statements

Write as an equation. Then solve (two more practice problems included): "When you add 16 to a number r, the sum is -5."

Practice the Skill Worksheet

Practice the Skill

Plenty of practice problems for you to work with. These problems flex your muscles on both addition and subtraction. Example: -15 - x = 43

Equations From Math Sentences Worksheet

Equations From Math Sentences

Write as an equation and then solve these math sentences. Example: The difference of 10 and a number is 23.

Equation Counters Worksheet

Equation Counters

The negative integers can be countered with positive integers and vice versa. Example: 9 - x = -24

Warm Up Worksheet

Warm Up

For these three problems: first simplify the side that does not have a variable present, then solve. Example: X + 13 = (-9) + 16

How to Solve Addition and Subtraction Equations

Mathematics is the bedrock that the entire world is built on. It allows us to understand how the world works, quantify everything, add a calculated value to it, and then compute it under different conditions. Two of the most basic ways to solve math equations are addition and subtraction.

Most of the mathematics we know follows these two forms of calculation. Understanding how to solve addition and subtraction equations will make mathematics simpler.


Addition and subtraction are two of the four pillars that mathematics stands on, the other two being multiplication and division. The concept of addition means increasing the existing number by introducing a new value to it. This means that if you have 5 apples, the addition of 4 more will bring the total number of apples up to 9.

The concept of multiplication also uses addition, bypassing the individual addition and simply taking the existing value and then increasing the value as many times as required, but with fewer steps.


A simple example of addition is 2 + 2 = 4

You take 2, add an additional 2 and get a result of 4. All of us know how this works.

As we move forward, we can add a variable to the equation e.g. 2 + a = 5

You take 2, add an unknown variable (a) and the result is 5. To solve this, we will use the addition principle which states that if one side of the equation is of a certain value, the other must be brought up to that same value for the equals-to sign to be justified.

To solve,

2 + a = 5
a = 5 - 2
a = 3


The process of subtraction is tied in with the concept of removing a certain amount from an existing value. For example, you have 10 apples in a crate. You take out 3 and are now left with 7. This is subtraction. Subtraction is addition done backward.


A simple example of subtraction is 3-2=1

You take 3, remove the 2 from it, and you are left with 1. This is simple and straightforward.

As we move forward, we add a variable to the equation and e.g. 3-a=2

Here, you take 3, subtract an unknown variable (a) and your answer is supposed to be 2. Once again, the addition principle will kick in and we will now balance out the equation to make both sides equal.

To solve.

3 - a = 2
3 - 2 = a
a = 1

To test this, we will insert the value of the variable into the original equation and get the same answer.

Addition and subtraction are among the most important pillars that the entire field of mathematics stands on. They take ordinary numbers and allow you to change them into completely new ones. By using addition and subtraction, it has become easier for the entire world to go from a basic society of cave-dwelling hunters into a species that is exploring the outer reaches of space. Without these functions and equations, much of the world around us would simply cease to exist.

It is important to understand how they work because at a basic level, they are rather simple. As you progress, they will begin to get more complex, and if you have a stable foundation, it will be easier for you to build up on it. Regardless of complexity, it will always have the same basic theory that is at work

It is time to explore the process of solving basic equations. All the work on these pages involve only sum and differences split into equations. The basic process that you want to follow includes three basic principles. Start by looking simplify both sides of the equation to the lowest form possible. You can do this by looking for like terms and combining them. If parentheses are present, work those all the way through. The next step is to counter any operators that exists. Just apply the opposite operator to both sides of the equation. The last step usually requires us to free the variable from any constants that are compounded with this. A simple multiplication or division on both sides will get this done for you. Make sure to check your answer by plugging the value into the original problem, if it works out you solved it.