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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.Question
Add the letters below together.StepbyStep:
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.
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.
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