Definition: A coefficient is the number multiplied by a variable in a term, such as the 9 in the term 9x.
What is a coefficient?
In a term like 9x, the number 9 is the coefficient. It tells how many copies of the variable you have.
How do you spot it?
Look at the number sitting right next to a variable. In the expression 4a – 7b + 12, the coefficients are 4 and -7. The 12 is a constant, not a coefficient. The sign belongs with the number, so the coefficient of -7b is -7.
What about hidden coefficients?
If a variable appears alone, its coefficient is 1. So y means 1y. And -z means -1z. For a fraction like x/3, the coefficient is 1/3.
Why do coefficients matter?
When you combine like terms, you add coefficients. For 5m + 2m, add 5 + 2 to get 7m. In an equation like 6x = 42, you divide by the coefficient 6 to isolate x.
What is the common mistake?
Forgetting the coefficient of 1. When simplifying t + 4t, the answer is 5t, not 4t.