Coefficient

Sommaire

In short: Coefficient names the number glued to a letter by multiplication, like the 7 in 7x or the -4 in -4y, and it is understood to be 1 when none is written.

6th GradeAlgebra6.EE.A.2b

What is Coefficient?

The coefficient is the multiplier sitting in front of a letter. In a cost rule such as $2.5g$, the 2.5 says how many dollars each gallon adds, while g is the changing amount.

Precisely, in the term $a x^n$ the number $a$ is the multiplier and it keeps its sign. The term $x$ has a value of 1 here and $-y$ has $-1$. A term without a variable, like 9, is a plain constant.

How to spot it

A word problem has a fixed price, speed or rate attached to a changing amount.
An expression has several pieces and you are asked for the number in front of one letter.
Pieces such as 5x and 9x are being combined by adding the numbers that sit in front.
A term looks like it has no number, such as m or -z.

The method

Pick out the term that contains the variable you care about.
Read the number multiplied by that variable, including its sign.
If no number is written, the value is 1; if only a minus sign is written, it is $-1$.
For a fraction like $\frac{3x}{4}$, the number is $\frac{3}{4}$.

In 6x – 4y + 11 the coefficients are 6 and -4.

Coefficient: solved example

Problem

A taco stand in San Antonio models its daily income as $I = 3.25t – 40$, where t is the number of tacos sold. Find the number multiplying t and say what it means.

Solution

The term with the variable is $3.25t$, so the multiplier is 3.25.

It is the price per taco: each taco sold adds \$3.25 to income, while the $-40$ is a daily cost that does not depend on t.

Try it

Question 1

What is the coefficient of m in $9 – m$?

Show the answer

$-m$ is $-1 \cdot m$, so it equals $-1$.

Question 2

List the multipliers of the letters in $\frac{2}{5}a + 7b – 0.5c$.

Show the answer

$\frac{2}{5}$, 7 and $-0.5$.

Coefficient vs. Variable

The multiplier is the fixed number and the variable is the letter that stands for something that can change. In $8p$, doubling p doubles the result, but the 8 stays put.

Variable

Keep going

Lessons

Writing and Reading Algebraic Expressions

Worksheets and quizzes

Related words

Whole dictionary: A–Z · 6th Grade · Algebra

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