AI Tutor
If a concert ticket costs xx dollars and you buy 6 tickets, you write the total cost as 6x6x. That number 6 scales the variable, telling you exactly how many times to count it.
A coefficient is the numerical factor multiplying a variable in an algebraic term. In the term 6x6x, the number 66 is the coefficient.
Spotting a number in front of a letter is easy, but what happens when a variable appears completely by itself?

The Hidden Multipliers

Because multiplying any quantity by 11 leaves it unchanged (1⋅x=x1 \cdot x = x), a standalone variable like xx has an invisible coefficient of 11.
Similarly, when you see a negative sign in front of a lone variable like −y-y, it represents (−1)⋅y(-1) \cdot y, making its coefficient −1-1.
What happens when terms involve subtraction or fractions? Let's look at how signs and division shape the coefficient.

Signs and Fractional Coefficients

The operational sign in front of a term always belongs to its coefficient. In the expression 4a−5b4a - 5b, the second term is −5b-5b, so the coefficient of bb is −5-5.
Dividing a variable by a number is identical to multiplying by a unit fraction: x3=13x\frac{x}{3} = \frac{1}{3}x, which means the coefficient is 13\frac{1}{3}.