Algebra Class: Components of Expressions

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Questions and Answers

What is the 8 in the expression $8y + 3$?

Variable

Coefficient (correct)

Constant

Term

What is the y in the expression $8y + 3$?

Constant

Term

Coefficient

Variable (correct)

What is the 3 in the expression $8y + 3$?

Coefficient

Term

Variable

Constant (correct)

Define a variable.

A letter that represents a number. Signup and view all the answers

Define a constant.

A number without a variable. Signup and view all the answers

Define a coefficient.

A number that is attached to a variable. Signup and view all the answers

Define an algebraic expression.

An expression containing a variable, numbers, and operations but no equal sign. Signup and view all the answers

What are numbers and variables separated by operations called?

Terms Signup and view all the answers

How many terms are in the expression $4x - 12$?

2 Signup and view all the answers

Which are like terms in the expression $6m - 2n + 7 - m$?

6m and -m Signup and view all the answers

How many terms are in the expression $6y$?

1 Signup and view all the answers

How many terms are in the expression $3 + 7x + 3x + x$?

4 Signup and view all the answers

How many terms are in the expression $6m - 2n + 7$?

3 Signup and view all the answers

List the coefficients in the expression $6m - 2n + 7$.

6, -2 Signup and view all the answers

List the coefficients in the expression $3 + 7x + 3x + x$.

7, 3, 1 Signup and view all the answers

List the constant in the expression $7x - 3 + x$.

-3 Signup and view all the answers

List the constant in the expression $6m - 2n + 7$.

7 Signup and view all the answers

List the variables in the expression $6m - 2n + 7$.

m, n Signup and view all the answers

List the variables in the expression $3 + 7x + 3x + x$.

x Signup and view all the answers

What are 2x and -5x in the expression $2x + 4 - 5x - 8$?

Like terms Signup and view all the answers

Study Notes

Algebraic Expression Components

Coefficient: A numerical factor of a term; e.g., in 8y + 3, 8 is the coefficient of y.
Variable: A symbol representing an unknown value, commonly a letter like y in expressions such as 8y + 3.
Constant: A fixed value without a variable; e.g., 3 in the expression 8y + 3.

Characteristics of Terms

Algebraic Expression: A combination of variables, numbers, and operations (like addition or subtraction) without an equal sign.
Term: Components of an algebraic expression, which include numbers and variables separated by operations. For example, in 4x - 12, both 4x and -12 are distinct terms.

Terms Count in Expressions

An expression such as 4x - 12 contains two terms.
The expression 6y consists of one term.
The expression 3 + 7x + 3x + x contains four terms.
The expression 6m - 2n + 7 has three terms.

Identifying Like Terms

Like terms share the same variable part; in the expression 6m - 2n + 7 - m, the like terms are 6m and -m.
In the expression 2x + 4 - 5x - 8, the like terms are 2x and -5x.

Coefficients and Constants Lists

For 6m - 2n + 7, the coefficients are 6 and -2.
In the expression 3 + 7x + 3x + x, the coefficients are 7, 3, and 1.
The constant in the expression 7x - 3 + x is -3, while in 6m - 2n + 7, it is 7.

Variables Identification

In the expression 6m - 2n + 7, the variables are m and n.
In 3 + 7x + 3x + x, the variable present is x.

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Description

Test your knowledge on the components of algebraic expressions, including coefficients, variables, and constants. Explore the characteristics of terms and identify like terms in various algebraic expressions. This quiz is designed to reinforce your understanding of fundamental algebra concepts.