One Step Equations

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One step equations require one “opposite” operation to be performed on them, which then allows us to obtain the value of their unknown variable.

The different types of one step equations and their opposites are shown below.

Opposites Table

Solving Addition and Subtraction Equations

These have already been covered in separate lessons on our blog.

Click the links below to visit these lessons.

One Step Addition Equations Lesson

One Step Subtraction Equations Lesson

Here are some reminder examples of how to do Addition and Subtraction Equations.

Add Example PPT Slide


Subtract Example PPT Slide


Solving Multiplication Equations

If our variable letter has a number directly in front of it, then this means it is multiplied by that number.

Eg. 3m means 3 times m or 3 x m or 3.m

The Opposite of Multiplication is Division.

To solve a multiplication equation, we DIVIDE BOTH SIDES by whatever number is in front of our variable letter.

Here is an example of how to solve a typical Multiplication Equation.

Multiply Example PPT Slide

The following short video shows how to do a Multiplication Equation.


Here is a more comprehensive video, that includes using a balance beam to represent the equation and solve it.


Here is a detailed video from Khan Academy about how multiplication by grouping actually works.


Solving Division Equations

If our variable letter has a number directly under it as a fraction, then this means it is divided by that number.

Eg. k/2 means k is divided by 2.

The Opposite of Division is Multiplication.

To solve a Division equation, we MULTIPLY BOTH SIDES by the number that our variable letter is being divided by.

Here is an example of how to solve a typical Division Equation.

Division Example PPT Slide

Here is a great video all about Division Equations.


The following video covers both Division and Multiplication Equations.


Solving Reciprocal Equations

Equations like 5n/4 = 10 can be solved by multiplying both sides by the reciprocal of 5/4.

The “Reciprocal of a fraction is that fraction turned “upside down”.

Eg. 5/4 has a reciprocal of 4/5.

The following video shows how to do Reciprocal type equations.

Equations like 5n/4 = 10, can also be solved using two opposite steps such as x 4 then divide by 5.

We will be looking at two step equations in a separate article on this blog.


One Step Equations Online Tests

The following question generator from Cool Math enables you to do as many practice questions as you like, and supplies answers at the click of a button.

Here is an online Quiz from BBC Maths on One Step Equations.

BBC One Step Equations Online Quiz

Here is an online quiz from Khan Academy that involves working out fraction answers for multiplication equations.


Interactive Online Activity

BBC Balance Scale Link

The following online interactive activity from BBC shows how simple equations can be solved using a balance beam scale.

It has a short introductory video, followed by some equations questions that we can try doing ourselves.


Related Items

How to Translate Word Problems into Equations
Solving One Step Addition Equations
Solving One Step Subtraction Equations
Two Step Equations Using Flowcharts and Back Tracking
Two Step Equations Using Reverse Operations
Three Step Equations Using Flowcharts and Back Tracking
Balance Beam Equations
Equivalent Equations
Fractions Equations
Solving Equations Word Problems
eBay Problem Solved Using Algebra Equations
Microsoft Mathematics Equations Solver
Equations Games

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