Variables and Expressions

A variable is a letter (like n, x, or y) that represents a number we don't know yet. An expression is a combination of numbers, variables, and operations.

Expression Examples

n + 5 — "a number plus 5"
3 × x or 3x — "3 times a number"
y - 2 — "a number minus 2"
2n + 1 — "double a number, then add 1"

Not an Expression

n + 5 = 12 — this is an equation (has an = sign)
An expression does NOT have an equals sign

Writing Expressions from Words

You can translate word descriptions into algebraic expressions. Look for key words that tell you which operation to use.

Words	Operation	Expression
"5 more than a number"	Addition	n + 5
"a number decreased by 3"	Subtraction	n - 3
"4 times a number"	Multiplication	4n
"a number divided by 2"	Division	n ÷ 2
"triple a number plus 7"	Multiply & Add	3n + 7

Evaluating Expressions

To evaluate an expression, replace the variable with a given number and calculate the result.

Example: Evaluate 3n + 2 when n = 4

Step 1: Replace n with 4: 3 × 4 + 2

Step 2: Multiply first: 12 + 2

Step 3: Add: 14

Solving Simple Equations

An equation has an equals sign. To solve it, find the value of the variable that makes the equation true. Use inverse operations (do the opposite).

Example: Solve n + 7 = 15

Step 1: The inverse of +7 is -7.

Step 2: n = 15 - 7

Answer: n = 8

Example: Solve 3x = 18

Step 1: The inverse of ×3 is ÷3.

Step 2: x = 18 ÷ 3

Answer: x = 6

Singapore Bar Model: Solving Equations

Problem: Sam has some stickers. He gets 8 more and now has 20. How many did he start with?

Equation: n + 8 = 20

Total: 20 stickers

n = ?

8

20

From the bar model: n + 8 = 20

So: n = 20 - 8 = 12

Answer: Sam started with 12 stickers.

Key Vocabulary

Variable

A letter that represents an unknown number (e.g. n, x, y).

Expression

A combination of numbers, variables and operations without an equals sign.

Equation

A statement with an equals sign showing two things are equal (e.g. n + 3 = 10).

Inverse Operation

The opposite operation used to undo another (+ undoes -, × undoes ÷).

Worked Examples

1

Write an expression: "I think of a number, double it, and add 6."

Step 1: Let the number be n.

Step 2: Double it: 2n

Step 3: Add 6: 2n + 6

2

Evaluate 5x - 3 when x = 4.

Step 1: Replace x with 4: 5 × 4 - 3

Step 2: Multiply first: 20 - 3

Answer: 17

3

Solve: 2n + 3 = 11

Step 1: Subtract 3 from both sides: 2n = 11 - 3 = 8

Step 2: Divide both sides by 2: n = 8 ÷ 2

Answer: n = 4

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

What is the value of 4n + 1 when n = 3?

8 12 13 7

Question 2

Which expression means "a number multiplied by 5 then subtract 2"?

n + 5 - 2 2n - 5 5(n - 2) 5n - 2

Question 3

Solve: n + 9 = 21

n = 12 n = 30 n = 10 n = 3

Question 4

Solve: 5x = 35

x = 30 x = 7 x = 40 x = 175

Question 5

Solve: 2n + 4 = 16

n = 10 n = 8 n = 6 n = 4

Algebraic Thinking