# 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 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.

# 1

Identify the coefficients of the letters.

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

# 3

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

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.

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.

The coefficient is multiplying the letter.

## 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.

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

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