Lesson 17: Translating Between Words and Algebraic Expressions

New Concept

Algebraic expressions, or variable expressions, are expressions that contain at least one variable. A numeric expression contains only numbers and operations.

What’s next

This lesson is your first step into that new language. Next, you’ll tackle worked examples on translating words into the symbols of algebra.

Property

Keywords like 'sum,' 'product,' 'difference,' and 'quotient' are direct commands that translate into the mathematical operations $+$, $-$, $\times$, and $\div$.

Examples

• "A number $y$ increased by 12" becomes $y + 12$.
• "The product of a number $x$ and 4" becomes $4x$.
• "The quotient of a number $m$ and 15" becomes $\frac{m}{15}$.

Explanation

Think of yourself as a math detective decoding a secret message! You are translating plain English into the language of algebra. Each keyword is a clue that tells you exactly which operation to use to build your expression and solve the puzzle.

Property

When you encounter the phrase "less than," the terms in the expression must be written in the reverse order of how you read them.

Examples

• "8 less than a number x" is written as $x - 8$.
• "James is 6 years younger than Lydia, who is x years old" becomes $x - 6$.

Explanation

Beware the flipper phrase! "8 less than x" doesn't mean $8-x$. It means you start with $x$ and then take 8 away. Always write the part after the word "than" first, then subtract the part that came before it.

Property

An algebraic expression like $m+7$ can be described in multiple ways, such as '7 more than m' or 'the sum of 7 and m'.

Examples

• "$y - 9$ can be '9 less than y' or 'the difference of y and 9'."
• "$5n$ can be 'the product of 5 and n' or '5 times n'."

Explanation

Time to be a math storyteller! Your job is to translate the expression back into English. There is often more than one correct way to describe the action, which lets you show off your vocabulary while explaining what the math is doing.