Algebraic Expressions • Topic 1 of 3

Writing Expressions from Word Problems

What is an Algebraic Expression?

An algebraic expression is a mathematical phrase that contains numbers, variables (letters), and operations (+, -, ×, ÷). It does NOT have an equals sign.

Variable: A letter that represents an unknown number (like x, y, n, a)

Key Words for Operations:

Operation	Key Words	Example	Expression
Addition (+)	plus, more than, sum, increased by, total	5 more than a number	x + 5
Subtraction (-)	minus, less than, difference, decreased by, fewer	3 less than a number	x - 3
Multiplication (×)	times, product, of, twice, triple	twice a number	2x
Division (÷)	divided by, quotient, half, split	half of a number	x/2 or x÷2

Important Order Notes:

"5 more than a number" → x + 5
"5 less than a number" → x - 5 (NOT 5 - x!)
"Twice a number" → 2x
"A number divided by 3" → x/3

TRANSLATING WORDS TO EXPRESSIONS - FLOWCHART:

    Word Phrase
         │
         ▼
    Identify the variable
    (what is unknown?)
         │
         ▼
    Identify the operation
    (look for key words)
         │
         ▼
    Write in correct order
    (watch for "less than"!)
         │
         ▼
    Algebraic Expression


COMMON PHRASES AND THEIR MEANINGS:

    "more than" → ADD (x + 5)
    "less than" → SUBTRACT but REVERSE! (x - 5, not 5 - x)
    "times" → MULTIPLY (3x)
    "divided by" → DIVIDE (x/4)
    "the sum of" → ADD (x + y)
    "the difference of" → SUBTRACT (x - y)
    "the product of" → MULTIPLY (x × y)
    "the quotient of" → DIVIDE (x ÷ y)


PRACTICE - FILL IN THE TABLE:

    Words                    Expression
    ──────────────────────────────────────────
    7 more than n            n + 7
    7 less than n            n - 7
    n more than 7            7 + n
    n less than 7            7 - n  (careful!)
    twice n                  2n
    n divided by 5           n/5
    4 times the sum of n and 3   4(n + 3)

Solved Examples

Worked Example

Write an expression for "5 more than twice a number"

Solution

"a number" = let it be x
"twice a number" = 2x
"5 more than" = add 5
Answer: 2x + 5

Worked Example

Write an expression for "7 less than a number"

Solution

"a number" = let it be n
"7 less than" means subtract 7 FROM the number
Answer: n - 7 (NOT 7 - n!)

Worked Example

Write an expression for "the sum of 3 times a number and 8"

Solution

"a number" = let it be y
"3 times a number" = 3y
"the sum of ... and 8" = add 8
Answer: 3y + 8

Worked Example

Write an expression for "four less than the product of 6 and a number"

Solution

"a number" = let it be a
"product of 6 and a number" = 6a
"four less than" = subtract 4
Answer: 6a - 4

Key Points

Variable = unknown number (use x, n, a, etc.)
"More than" and "less than" are DIFFERENT orders
"Less than" flips the order: n - 5, not 5 - n
Multiplication: 2x means 2 × x
Parentheses group operations: 3(x + 4)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1."$5$ more than $x$" is written as:

Explanation: $x+5$.

Q2."Twice a number $x$" is:

Explanation: $2x$.

Q3."A number decreased by $3$" is:

Explanation: $x-3$.

Q4.A variable represents:

Explanation: An unknown.

Practice more MCQs → 📝 Assignment · 35 marks