# Subtraction Equations

In the image above, we have photographically reversed the picture of the basketballs. We did this to emphasize that working with equations involves making things the opposite to what they are currently.

For equations which have a number ADDED to a letter, we SUBTRACT away that number to find out the value of the letter “variable”.

For equations which have a number SUBTRACTED from the letter, we ADD that same number to both sides of the equation. This will allow us to find out the number value of our letter “variable”.

Variables

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“Variables” are Algebra letters like x, y, n, T, P, A, etc, that represent an unknown value in a word problem.

Variables are also used when writing computer programs. A variable letter can only represent one item, which means variables like “Cats&Dogs” are not allowed.

Typical Variables in maths questions might be values such as:

c = number of cats
d = number of dogs
T = the total number of animals
P = Price after discount has been applied
d = Dollar amount spent
I = Interest on a credit card
b = the number of boys in a class
A = Cheryl’s current age
n = the number of pizzas for 20 people

and so on.

We use letter values (or variables) in our maths sums, because it is much easier than writing out long groups of words.

Variables are letters that are used to represent unknown items in our maths questions.

We solve Algebra Equations so that we can find out the number values of these variables.

One Step Subtraction Equation

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A typical example involving a subtraction equation is the following situation.

In our Sports Store we sold 27 basketballs today, and we now have 11 basketballs left on the shelf.

How many basketballs did we have at the start of the day?

First we write a word equation to represent the situation.

Let “T” equal the Total Basketballs at the start of the day.

We know that:

By substituting the above three values into our original word equation, we can create the following Algebra equation:

T – 27 = 11

Our next step is to investigate what is happening to the the unknown letter value “T”.

In the equation, T has 27 SUBTRACTED from it.

To solve our equation we do the opposite of Subtracting, (which is Adding), to both sides of the equals sign.

But how much do we add to each side of the equation ?

T – 27 = 11

To obtain our final answer, we need to get “T” on its own, by eliminating the – 27 that is with it.

We can get rid of the – 27 by ADDING 27, so we need to add 27 to both sides of the equation.

T – 27 = 11
T – 27 + 27 = 11 + 27
————-
T + 0 = 38
T = 38

————-

At the start of the day we had 38 basketballs in our shop.

We can check our answer by substituting all our values into the original equation, and seeing if the equation ends up the same on both sides.

38 – 27 = 11

11 = 11

By doing the substitution check shown above, we can be completely certain that the start of day total of 38 is the correct answer to our maths question.

Video Lessons on One Step Subtraction Equations

Here is a short video by “Your Teacher” which shows the steps required to solve a one step subtraction linear equation.

Here is a more comprehensive video about solving Single Step Addition and Subtraction equations.

Note in this video that the Americans call a “see-saw” balancing toy, a “teeter-totter” !

The following video covers doing one step Add and Subtract equations that involve Integers.

Here is another video lesson on equations that involve Integers.

One Step Subtraction Equations Worksheets

The following worksheets have questions to do on Subtraction Equations. Answers are available when we scroll down to page 2 on each sheet.

The first sheet is very easy, the second and third sheets have negative numbers, the fourth sheet has Year 8 type questions.

Subtraction Equations Worksheet 1

Subtraction Equations Worksheet 2

Subtraction Equations Worksheet 3

Subtraction Equations Worksheet 4

Here is a Speed Test Video that you can do to get fast at solving one step equations.

That’s it for one step Subtraction equations.

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