Question

an algebraic ______ is a symbolic expression that shows the operations to be performed on terms.
a ______ is a symbol, usually a letter, that represents an unknown number in an expression or an equation.
the numerical factor of a term that contains a variable is called a ______.
a ______ is a number on its own, or sometimes a letter that stands for a fixed number in an equation.
the ______ in an expression are the plus, minus, times, or divided by signs.
an equation is a statement that two algebraic expressions are ______.
a ______ term does not contain any variables.
______ terms are terms that have the same variable and exponent.
the ______ is the operation between terms in an expression or sides of an equation.

Explanation:

To solve these fill - in - the - blank questions about algebraic concepts, we analyze each one based on the definitions of algebraic terms:

1. First blank:

An algebraic expression is a symbolic expression that shows the operations to be performed on terms. By the definition of an algebraic expression, it is a combination of terms with operations, so this blank is filled with "expression".

2. Second blank:

A variable is a symbol, usually a letter, that represents an unknown number in an expression or an equation. Variables are used to represent quantities that can change or are unknown, so this blank is "variable".

3. Third blank:

The numerical factor of a term that contains a variable is called a coefficient. For example, in the term \(3x\), 3 is the coefficient (the numerical part with the variable \(x\)), so this blank is "coefficient".

4. Fourth blank:

A constant is a number on its own, or sometimes a letter that stands for a fixed number in an equation. Constants have a fixed value, so this blank is "constant".

5. Fifth blank:

The operations in an expression are the plus, minus, times, or divided by signs. These are the arithmetic operations that combine terms, so this blank is "operations".

6. Sixth blank:

An equation is a statement that two algebraic expressions are equal. The key property of an equation is that the expressions on either side have the same value, so this blank is "equal".

7. Seventh blank:

A constant term does not contain any variables. A constant term has a fixed value and no variable part, so this blank is "constant".

8. Eighth blank:

Like terms are terms that have the same variable and exponent. For example, \(2x\) and \(5x\) are like terms as they have the same variable \(x\) with the same exponent (1 in this case), so this blank is "like".

9. Ninth blank:

The operation is the operation between terms in an expression or sides of an equation. This is similar to the fifth question, referring to the arithmetic operation (like +, -, ×, ÷) between terms or sides, so this blank is "operation".

Final Answers (in order of the blanks):

1. expression
2. variable
3. coefficient
4. constant
5. operations
6. equal
7. constant
8. like
9. operation

Answer:

To solve these fill - in - the - blank questions about algebraic concepts, we analyze each one based on the definitions of algebraic terms:

1. First blank:

An algebraic expression is a symbolic expression that shows the operations to be performed on terms. By the definition of an algebraic expression, it is a combination of terms with operations, so this blank is filled with "expression".

2. Second blank:

A variable is a symbol, usually a letter, that represents an unknown number in an expression or an equation. Variables are used to represent quantities that can change or are unknown, so this blank is "variable".

3. Third blank:

The numerical factor of a term that contains a variable is called a coefficient. For example, in the term \(3x\), 3 is the coefficient (the numerical part with the variable \(x\)), so this blank is "coefficient".

4. Fourth blank:

A constant is a number on its own, or sometimes a letter that stands for a fixed number in an equation. Constants have a fixed value, so this blank is "constant".

5. Fifth blank:

The operations in an expression are the plus, minus, times, or divided by signs. These are the arithmetic operations that combine terms, so this blank is "operations".

6. Sixth blank:

An equation is a statement that two algebraic expressions are equal. The key property of an equation is that the expressions on either side have the same value, so this blank is "equal".

7. Seventh blank:

A constant term does not contain any variables. A constant term has a fixed value and no variable part, so this blank is "constant".

8. Eighth blank:

Like terms are terms that have the same variable and exponent. For example, \(2x\) and \(5x\) are like terms as they have the same variable \(x\) with the same exponent (1 in this case), so this blank is "like".

9. Ninth blank:

The operation is the operation between terms in an expression or sides of an equation. This is similar to the fifth question, referring to the arithmetic operation (like +, -, ×, ÷) between terms or sides, so this blank is "operation".

Final Answers (in order of the blanks):

1. expression
2. variable
3. coefficient
4. constant
5. operations
6. equal
7. constant
8. like
9. operation