Writing Algebraic Expressions

One of the most important algebra skills is translating words into math.

Key Translation Words

Addition (+)

• sum
• plus
• more than
• increased by
• total

Example: "5 more than a number" → $x + 5$

Subtraction (−)

• difference
• minus
• less than
• decreased by
• fewer

Example: "a number decreased by 3" → $x - 3$

⚠️ Watch out: "5 less than a number" is $x - 5$, not $5 - x$

Multiplication (×)

• product
• times
• of
• multiplied by
• twice, triple

Example: "twice a number" → $2x$

Division (÷)

• quotient
• divided by
• per
• ratio

Example: "a number divided by 4" → $\frac{x}{4}$

Practice Translations

Words	Expression
The sum of a number and 8	$x + 8$
7 less than a number	$x - 7$
Triple a number	$3x$
A number divided by 5	$\frac{x}{5}$
4 more than twice a number	$2x + 4$
Half of a number minus 3	$\frac{x}{2} - 3$

Complex Expressions

Sometimes you need to combine operations:

"3 times the sum of a number and 2"

1. "sum of a number and 2" = $x + 2$
2. "3 times that" = $3(x + 2)$

"5 less than the product of 4 and a number"

1. "product of 4 and a number" = $4x$
2. "5 less than that" = $4x - 5$