Expressions

Expressions Unit Test Review

Content

• Identify parts of an algebraic expression

• Apply math properties to generate equivalent expressions

• Translate algebraic expressions

• Simplify algebraic expressions

• Evaluate algebraic expressions

Key Points to Remember

• In algebra, we normally do not write the multiplication sign between a number and a variable. For example, we write 

  4×a as 4𝑎.

• In algebra, we normally do not write down the plus sign in front of the very first term.

• In algebra, we normally do not write down the number 1 if it is the coefficient of a variable.

• When there are constants in an expression, treat them as like terms.

Types of Expressions

• Numerical expression: an expression that contains only numbers and operations.

• Algebraic expression: an expression that contains variables, numbers, and operations

Parts of an Algebraic Expression

-An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators. It does not have an equals sign.

-Terms are always separated by addition and subtraction signs not multiplication and division signs.

Multiple Choice

A ______________ is a term without a variable. It can have a negative value (if it has a minus sign in front of it) or a positive value (if it has a plus sign or no sign in front of it).

• constant

• coefficient

• variable

• term

Multiple Choice

The _______________ is the number (factor) being multiplied by the variable. It can have a negative value (if it has a minus sign in front of it) or a positive value (if it has a plus sign or no sign in front of it).

• coefficient

• constant

• variable

• term

Multiple Choice

A _________ can be a single number (positive or negative), or a variable, or one or more numbers and variables that are being multiplied together.

• variable

• term

• constant

• coefficient

Multiple Choice

A ___________ is a symbol used to represent a number in an expression. It is usually a letter of the alphabet.

• constant

• coefficient

• term

• variable

Multiple Choice

7n - 4b + 2y - 59

How many terms are in this expression?

• 4

• 3

• 8

• 6

Multiple Choice

7n - 4b + 2y - 59

What term is the constant in the expression?

• 7n

• -4b

• 2y

• -59

Multiple Choice

7n - 4b + 2y - 59

How many positive coefficients are in the expression?

• 2

• 3

• 1

• 4

Multiple Choice

7n - 4b + 2y - 59

How many negative coefficients are in the expression?

• 4

• 3

• 2

• 1

Multiple Choice

7n - 4b + 2y - 59

What are the variables in the expressions?

• n, -b, y

• -n, -b, -y

• n, b, y

Equivalent Expressions

-have the same value

-may not contain the same numbers

-are created using math properties

Multiple Select

Which expressions are equivalent to

7x + 9 ?

• 3x + 9 - 4x

• 3x + 9 + 4x

• 6 + 8x - x + 3

• 9x + 4 -2x + 5

Multiple Select

Which expressions are equivalent to 24x -18?

• 6(4x −3)

• 6

• 4(6x – 4)

• 2(12x − 9)

Multiple Select

Which expressions are equivalent to

6y + 2b?

• 2b + 6y

• 3b + b + 6y

• 5b + 3y - 3b + 3y

• 9y + 2b - 4y

Translate words to Algebraic Expressions

Expressions can be translated from words to algebraic expressions by identifying key words that indicate operations and order of the terms.

Multiple Choice

the quotient of a number and thirty-six

• $$\frac{36}{b}$$  

• $$\frac{b}{36}$$  

• $$36b$$  

• $$b36$$  

Multiple Choice

the product of a number and twenty-fix

• $$a-25$$

• $$\frac{a}{25}$$

• $$a\ +\ 25$$

• $$25a$$

Multiple Choice

eight less than a number

• $$8-m$$

• $$8m$$

• $$m-8$$

• $$m\ +\ 8$$

Multiple Choice

the sum of a number and nine

• $$v\ +\ 9$$

• $$v-\ 9$$

• $$9v$$

• $$\frac{v}{9}$$

Multiple Choice

three times the sum of a number and fifteen

• $$3\left(\ x\ +\ 15\right)$$

• $$3x\left(\ x\ +\ 15\right)$$

• $$3\left(\ x\ -\ 15\right)$$

• $$3x\left(x-15\right)$$

Multiple Choice

eight times a number minus four

• $$8d\ +\ 4$$

• $$8\left(x-4\right)$$

• $$8d\ -\ 4$$

• $$8\left(x\ +\ 4\right)$$

Simplifying Algebraic Expressions

To simplify an expression is to give it in its simplest form. We do this by collecting (combining) like terms using addition or subtraction.

Multiple Choice

Simplify the expression

10x – 8x + 2 + 10

• 18x + 12

• 2x + 12

• 2x + 8

• 30x

Multiple Choice

Simplify the expression

3a + 7 + 2(3 + a)

• 5a + 7

• 4a + 7

• 18a

• 5a + 13

Multiple Choice

Simplify the expression

2s + 10 – 7s – 8 + 3s – 7

• -2s - 5

• 2s - 5

• 37s

• 12s - 25

Evaluate Algebraic Expressions

The process of replacing the variables in an expression with the numerical values and simplifying 

Multiple Choice

Evaluate the expression if x = 5 and y = 2

• 15

• 5

• 57

• -5

Multiple Choice

Evaluate the expression if r = 5 and s = -3

• 14

• 11

• -14

• -11

Multiple Choice

Evaluate the expression if t= -10

• $$-10\ \frac{2}{3}$$

• -16

• $$10\ \frac{2}{3}$$

  
  

• 16

Multiple Choice

Evaluate the expression if 

$$z\ =-\frac{1}{2}$$  

• $$-\frac{375}{8}$$  

• $$47\ \frac{1}{8}$$  

• $$-47\ \frac{1}{8}$$  

• $$\frac{375}{8}$$