Adding Letters in Algebra
(KS3, Year 7)

The Lesson

Letters can be added to numbers, other letters and the same letter.
  • A letter can be added to a number.

    a plus 2
  • A letter can be added to another letter.

    a plus b
  • A letter can be added to the same letter.

    a plus a When the same letter is added to itself, we can simplify the expression:

    a plus a equals 2a

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.
a plus 3a

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.

1 plus 3 equals 4

3

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

4a

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.
a plus 2 plus b plus 3a Let's work left to right.
  • When a letter is added to a number, we cannot simplify any further. Leave it as a + 2.

    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.

    a + 2 + b
  • We are adding 3a. This is the same letter as the a in the expression.

    a + 2 + b + 3a We have seen that a + 3a = 4a.

    4a + 2 + b
We have added the letters and numbers:
a + 2 + b + 3a = 4a + 2 + b

Lesson Slides

The slider below shows a real example of how to add letters in algebra. Open the slider in a new tab

Adding Like Terms in Algebra

A letter is a like term with itself. Adding a letter with the same letter is adding like terms.

What Is a Coefficient?

A coefficient is a number that is placed in front of a letter.

2 a and 3 a The coefficient is multiplying the letter.

2 a equals 2 times a. 3 a equals 3 times a

A Letter without a Number in Front of It Has a Coefficient of 1

Sometimes a letter will not have a number in front of it.

a
Don't be fooled. It still has a coefficient. The coefficient is 1.

1 a
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See Also

What is algebra? What is a coefficient? What is a like term in algebra? Adding like terms in algebra