The LessonLetters 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 LetterWe have just seen that a + a = 2a. If we add one a to one a, we get two a's.
a + a = 2aThe 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) = 3aTo 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 LetterAdding the same letters to each other is easy, even when they have coefficients.
QuestionAdd the letters below together.
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.
Add the coefficients together.
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 LettersLet's put what we have learned together.
QuestionAdd 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
Lesson SlidesThe slider below shows a real example of how to add letters in algebra.
Adding Like Terms in AlgebraA 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 1Sometimes a letter will not have a number in front of it.
Don't be fooled. It still has a coefficient. The coefficient is 1.