The LessonLetters can be subtracted with numbers, other letters and the same letter.
- 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 LetterWe have just seen that 2a − a = a. If we take one a from two a's, we are left with one a.
2a − a = aThe 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 = 2aTo subtract the same letters from each other, subtract the coefficients of the letters from each other and place that number in front of the letter. (The same letters are like terms).
How to Subtract a Letter from the Same LetterSubtracting the same letters from each other is easy, even when they have coefficients.
QuestionSubtract the letters below from each other.
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.
Subtract the coefficients from each other.
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 AlgebraLet's put what we have learned together.
QuestionSubtract 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
Lesson SlidesThe slider below shows a real example of how to subtract letters in algebra. Open the slider in a new tab
Subtracting Like Terms in AlgebraA 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 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.