Variables and Algebraic Expressions

Variables

These are letters or symbols holding the place of an unknown number in mathematics.

Multiple Choice

Which is the variable in the following expression: $$5t\ -2$$

• 2

• 14

• t

• 5

Multiple Choice

$$5p\ -\ m\ +6$$  

How many variables are in the following expression:

• 2

• 1

• 5

• 4

Multiple Choice

$$2m^2+m-2y$$  

How many variables are in the following expression:

• 4

• 2

• 5

• 3

Introduction to Writing Algebraic Expressions

What is an Expression

 An expression is a phrase made up of numbers, operation symbols, and sometimes variables. 

A variable is a letter that represents an unknown number. When you multiply a number by a variable, you do not need a multiplication sign between the two. You can write the number directly in front of the variable.

 This number multiplied by the variable is called the coefficient.

Let's look at an expression...

Multiple Choice

Algebraic expressions can have a variable, operational symbols, and numbers?

• True

• False

Multiple Choice

Click on the name of the red part of the algebraic expression:

4² + 2x -7

• constant

• variable

• coefficient

• term

Multiple Choice

Click on the name of the red part of the algebraic expression:

4² + 2x -7

• variable

• constant

• base

• coefficient

Multiple Choice

Click on the name of the red part of the algebraic expression:

4 (x-2) -12

• constant

• variable

• coefficient

• exponent

Key Words in Algebraic Expressions

Addition: sum, more, more than, plus, increased by, gain

Subtraction: difference, less, less than, minus, decreased by, loss

Multiplication: product, multiplied by, times, double, triple

Division: quotient, divided by, per, ratio, half, third, fourth, into, equal groups

Exponents: times itself, squared, cubed

The sum of five and a number.

Step 1. What are the key words?

Step 2. What are the numbers/variables?

Step 3. Write out the expression.

Multiple Choice

The Sum of 5 and a Number

• 5 - x
• 5x

• 5÷x

• 5 + x

Ten less than a number

What are the key words?

Step 1. What are the key words?

Step 2. What are the numbers/variables?

Step 3. Write out the expression

Multiple Choice

Ten less than a number

• x + 10
• 10 - x
• x - 10
• 10x

Multiple Choice

Which phrase represents "the sum of 11 and a number".

• 11-x

• 11+x

• -11+1

• -11-x

Multiple Choice

Choose the right expression for "the difference of three and a number".

• 3x

• 3-x

• x-3

• $$\frac{3}{x}$$

Multiple Choice

w increased by 5

• w - 5
• 5w
• w + 5
• w / 5

Multiple Choice

Fourteen subtracted from a number written as an expression is

• 14-x

• x-14

• x/14

• 14+x

There are many ways to write a multiplication and division expression.

Multiple Choice

twenty times a number

• 20 + x

• x - 20

• 20x

• x/20

Multiple Choice

the quotient of seven and a number

• 7/x

• x/7

• x - 7

• 7 - x

Multiple Choice

ten divided by a number

• x + 10

• 10 - x

• 10/x

• x/10

Multiple Choice

the quotient of a number and twelve

• x + 12

• x - 12

• 12/x

• x/12

Multiple Select

Write a verbal expression for:

2a+6

• 6 more than the product of 2 and a number

• 6 less than the product of 2 and a number

• 6 more than the quotient of 2 and a number

• twice a number plus 6

Multiple Select

What word phrase can you use to represent "5x + 2"?

• 5 times a number plus 2

• 2 more than the product of 5 and a number

• a number times the sum of 5 and 2

• the sum of 5 times a number and 2

Multiple Choice

Translate this phrase into an algebraic expression.

2 times the sum of a number and 15

Use the variable B to represent the unknown number.

• 2(B+15)

• 2B+15

• 2B×15

• 2×15B

Algebraic Expressions and word problems

Fill in the Blanks

Write the Expression to Represent This Situation

Multiple Choice

Tia has 15 dresses. One day, she buys "d" more dresses. Write an expression for the new number of dresses.

• 15 + d

• 15d

• 15 - d

Fill in the Blanks

Write an Expression to Represent this Situation

Fill in the Blanks

Ty signed up for a gym membership. There is a one-time fee of $40 and a cost of $10 per month. Write an algebraic expression for the cost for "m" months.

Fill in the Blanks

Write an Expression to Represent This Situation

Multiple Choice

Strawberries are $1.95 a pound. Write an expression for p pounds of strawberries. 

• $1.95+p
• $1.95-p
• $1.95/p
• $1.95p

Multiple Choice

Jamal helped his grandmother plant her vegetable garden. He planted 3 rows of zucchini seeds and 4 rows of yellow squash seeds. Each row had s seeds. Which expression represents how many seeds Jamal planted in all?

• 3s + 4s

• 3s + 4

• 4s + 3

• 34s

Multiple Choice

If c represents the cookies the Joe bought, which expression shows how much he split between himself and 3 siblings?

• $$\frac{c}{4}$$

• $$4c$$

• $$c\ +\ 4$$

• $$c\ -\ 4$$