Writing Algebraic Expressions

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.

Multiple Choice

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

• True

• False

Let's look at an expression...

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

Multiple Select

Finding these words in an expression means to subtract: sum, more, more than, plus, increased by, gain

• True

• False

Multiple Select

Finding these words in an expression mean to subtract: difference, less, less than, minus, decreased by, loss

• true

• false

Lets Look at some Examples

Write five plus three times itself as an expression.

Step 1. What are the key words?

Step 2. What are the terms/numbers?

Step 3. Write out the expression.

So we get 5 + 3²

The sum of five and four.

Step 1. What are the key words?
Step 2. What are the numbers/variables?
Step 3. Write out the expression.

5+4

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

n - 10

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.

For example, the word "product" tells us to use multiplication. So, the phrase
"the product of 8 and k" can be written as

 $8k$  ,  it means the same as  $8\ \times\ k$  or  $8\cdot k$  

Write an expression for "x divided by 9" can be written as

 $\frac{x}{9}$ , it means the same as  $x\div9\$  or x/9

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