The exact answer to the question 'What is the coefficient of y in 15xy?' is 15.
Understanding Coefficients in Algebraic Expressions
In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable (or variables) in an algebraic expression. It essentially tells you how many of a particular variable or group of variables you have.
For instance:
- In the term
7x
, the coefficient ofx
is7
. - In the term
-3z
, the coefficient ofz
is-3
.
Coefficients can be numbers, letters (representing constants), or even other variables, depending on what part of the term you are defining as the variable. However, when generally asked for "the coefficient," it often refers to the numerical part.
Analyzing the Term 15xy
Let's break down the algebraic term 15xy
:
- 15 is the numerical factor (a constant).
- x is a variable.
- y is a variable.
The term 15xy
represents the product of 15
, x
, and y
. When you are asked for the coefficient of a specific variable, like y
, you identify the factor that multiplies y
.
While the expression 15xy
can be seen as (15x) * y
, implying that 15x
is the factor multiplying y
, in many contexts, especially when seeking "the coefficient" of a single variable in a multi-variable term, the numerical constant associated with it is the intended answer. In this specific case, the numerical value that is a part of the constant multiplier for y
is 15
. This interpretation is supported by established mathematical references, which state that the coefficient of y
in 15xy
is 15
.
Examples of Identifying Coefficients
Identifying coefficients is a fundamental skill in algebra. Here are a few examples to illustrate:
Algebraic Term | Variable/Term of Interest | Coefficient | Explanation |
---|---|---|---|
7x |
x |
7 |
The number multiplying x is 7 . |
-5ab |
ab |
-5 |
The number multiplying the product ab is -5 . |
15xy |
y |
15 |
The numerical factor associated with y is 15 . |
pqr |
pqr |
1 |
When no number is visible, the coefficient is 1 . |
z/2 |
z |
1/2 |
z/2 can be written as (1/2)z . |
Importance of Identifying Coefficients
Accurately identifying coefficients is crucial for various algebraic operations, including:
- Combining like terms: Only terms with the same variables and powers can be combined by adding or subtracting their coefficients.
- Solving equations: Understanding coefficients helps isolate variables.
- Factoring expressions: Coefficients play a key role in finding common factors.
- Understanding proportionality: Coefficients often represent rates or constants of proportionality in real-world applications.