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Adding Letters in Algebra

(KS3, Year 7)

Letters can be added to numbers, other letters and the same letter.

A letter can be added to a number.
A letter can be added to another letter.
A letter can be added to the same letter. When the same letter is added to itself, we can simplify the expression:

Adding a Letter to the Same Letter

We have just seen that a + a = 2a. If we add one a to one a, we get two a's.

a + a = 2a

The 2 in front of the a is the coefficient. It tells you how many a's we have. We can add a letter to the same letter even if the letters have coefficients in front of them. Imagine we wanted to add a to 2a. If we add one a to two a's, we get three a's.

a + 2a = a + (a + a) = 3a

To add the same letters together, add the coefficients of the letters together and place the sum in front of the letter. (The same letters are like terms).

How to Add a Letter to the Same Letter

Adding the same letters to each other is easy, even when they have coefficients.

Question

Add the letters below together.

Step-by-Step:

1

Identify the coefficients of the letters. The coefficient of a is 1. The coefficient of 3a is 3

Don't forget: If a letter does not have a number in front of it, its coefficient is 1.

2

Add the coefficients together.

3

Make the number found in Step 2 (4) the coefficient of the letter (a).

Answer:

We have added the letters:

a + 3a = 4a

A Real Example of How to Add a Letters

Let's put what we have learned together.

Question

Add the letters and numbers below together.

Let's work left to right.

When a letter is added to a number, we cannot simplify any further. Leave it as a + 2.
We are adding b, a different letter, to a and 2. We can not simplify any further. Leave it as a + 2 + b.
We are adding 3a. This is the same letter as the a in the expression. We have seen that a + 3a = 4a.