# Subtracting Letters in Algebra

(KS3, Year 7)

- A number can be subtracted from a letter. A letter can be subtracted from a number.
- A letter can be subtracted from another letter.
- A letter can be subtracted from the same letter. When the same letter is subtracted from itself, we can simplify the expression:

## Subtracting a Letter from the Same Letter

We have just seen that**2a**−

**a**=

**a**. If we take one

**a**from two

**a**'s, we are left with one

**a**.

**2a**−

**a**=

**a**

**2**in front of the

**a**is the coefficient. It tells you how many

**a**'s we have.

(

**2a**=

**2**×

**a**=

**a**+

**a**). We can subtract a letter from the same letter even if the letters have coefficients in front of them. Imagine we wanted to subtract

**a**from

**3a**. If we subtract one

**a**from three

**a**'s, we get two

**a**'s.

**3a**−

**a**= (

**a**+

**a**+

**a**) −

**a**=

**2a**

## How to Subtract a Letter from the Same Letter

Subtracting the same letters from each other is easy, even when they have coefficients.## Question

Subtract the letters below from each other.## 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

Subtract the coefficients from each other.

## 3

Make the number found in

**Step 2**(2) the coefficient of the letter (a).## Answer:

We have subtracted the letters:**3a**−

**a**=

**2a**

## A Real Example of How to Subtract Letters in Algebra

Let's put what we have learned together.## Question

Subtract the letters and numbers below together.-
When a letter is subtracted from a number, we can not simplify any further. Leave it as
**3a**−**2**. -
We are subtracting
**b**, a different letter, from**a**and**2**. We can not simplify any further. Leave it as**3a**−**2**−**b**. -
We are subtracting
**a**. This is the same letter as the**3a**in the expression. We have seen that**3a**−**a**=**2a**.

**3a**−

**2**−

**b**−

**a**=

**2a**−

**2**−

**b**

## Subtracting Like Terms in Algebra

A letter is a like term with itself. Subtracting a letter with the same letter is subtracting 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