Lesson 3: Writing Algebraic Expressions from Words

Property

Translating word phrases into algebraic expressions involves identifying keywords that signify mathematical operations.

• Addition: sum, more than, plus, increased by
• Subtraction: difference, less than, minus, decreased by
• Multiplication: product, times, twice
• Division: quotient, divided by

Examples

• Translate "the product of 4 and a number x" into an expression. The keyword "product" means multiplication, so the expression is $4x$.

Property

To translate verbal phrases that group quantities, use parentheses $()$. Phrases like "the sum of..." or "the difference between..." that are then multiplied or divided require parentheses to ensure the addition or subtraction is performed first. For example, "the sum of $a$ and $b$, times $c$" is written as $(a + b) \times c$.

Examples

Property

Algebraic expressions may involve two or more operations. Some algebraic expressions involve more than one variable. To write an algebraic expression from a phrase, we must identify the unknown quantities, assign variables to represent them, and then translate the mathematical operations.

Examples

• A delivery service charges 8 dollars per package plus a 10 dollar flat fee. The total cost for $p$ packages is $8p + 10$.

• The total number of books read by Leo and Mia can be represented by $L + M$, where $L$ is the number of books Leo read and $M$ is the number Mia read.