# Adding Letters in Algebra

(KS3, Year 7)

- 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**

**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**

## 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.

**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.-
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**.

**a**+

**2**+

**b**+

**3a**=

**4a**+

**2**+

**b**

## 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**.

## Worksheet

This test is printable and sendable