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Chapter 1: Problem 15

In each term, give the numerical coefficient of the variable(s). $$ 3 m^{2} $$

Short Answer

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Step by step solution

01

Identify the Numerical Coefficient

The numerical coefficient is the number that is multiplied by the variable(s). In this term, the term is written as: \[3 m^{2}\]
02

Isolate the Numerical Coefficient

From the term \[3 m^{2}\], identify the number in front of the variable. The variable part is \(m^2\).
03

Determine the Coefficient

The number directly in front of \(m^2\) is 3. Therefore, the numerical coefficient is 3.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Algebraic Expressions
An algebraic expression is a mathematical phrase that includes numbers, variables, and operation symbols like addition or multiplication. These expressions are the foundation of algebra.
For example, in the expression [3 m^2] , we see a combination of a number (3), a variable (m), and an exponent (2).
Algebraic expressions can be as simple as a single number or variable, or they can be complex with multiple terms.
Understanding how to break down these expressions is crucial in algebra.
Each part of the expression has its role. Here, '3' is the coefficient; 'm' is the variable, and the exponent '2' shows that the variable is squared.
The Role of Variables
Variables are symbols, often letters, used to represent unknown values or values that can change.
In algebraic expressions, they allow us to generalize and solve problems for many different scenarios.
For instance, in [3 m^2] , 'm' is the variable. It could be any number, and the expression tells us that once we know 'm', we square it and multiply the result by 3.
This flexibility makes variables powerful tools in mathematics.
They are essential for creating formulas and equations, which can model real-world situations like calculating interest or predicting future values.
What are Coefficients?
A coefficient is the numerical part of a term in an algebraic expression. It is the number that multiplies the variable.
In algebra, understanding coefficients is vital because they indicate the magnitude or how many times the variable is to be counted.
For example, in [3 m^2] , 3 is the coefficient. It tells us that whatever value 'm^2' represents, it should be multiplied by 3.
Identifying coefficients helps in simplifying and solving algebraic expressions and equations.
You鈥檒l often encounter terms with different coefficients, and recognizing them allows you to combine like terms and perform other operations efficiently.

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Most popular questions from this chapter

Simplify each expression. $$ -5(8 x+2)-(5 x-3)-3 x+17 $$

Write a numerical expression for each phrase and simplify. Nine subtracted from the product of 1.5 and \(-3.2\)

Simplify each expression. $$ -2(-3 k+2)-(5 k-6)-3 k-5 $$

Decide whether each statement is an example of the commutative, associative, identity, inverse, or distributive property. See Examples \(1,2,3,5,6,7,\) and \(9 .\) $$2(x+y)=2 x+2 y$$

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(18,12,0,-4,\) and \(-10\)
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