Writing and Interpreting Expressions

Have you ever noticed that math is like its own language? Just like we use words to build sentences, we use numbers and symbols to build numerical expressions. In this lesson, you will learn how to translate regular words into math expressions, and how to explain what a math expression means—all without actually having to solve it!

Translating Words into Math

When writing an expression from a word phrase, look for clue words that tell you which operation to use:

• Addition ($+$): sum, add, increased by, more than
• Subtraction ($-$): difference, subtract, decreased by, less than
• Multiplication ($\times$): product, multiply, times, twice
• Division ($\div$): quotient, divide, half

Often, you will need to use parentheses $()$ to show that one part of the math needs to happen first.

Example 1: "Add 5 and 7, then multiply by 3" First, we need to add 5 and 7. To make sure this addition happens first, we put it inside parentheses: $(5 + 7)$. Then, we multiply that result by 3. Expression: $(5 + 7) \times 3$

Example 2: "Twice the sum of 6 and 8" "The sum of 6 and 8" means we add them together: $(6 + 8)$. "Twice" means we multiply that whole sum by 2. Expression: $2 \times (6 + 8)$

Interpreting Math Expressions

Interpreting an expression means looking at the numbers and symbols and describing what is happening using words. You don't need to find the final answer; you just need to explain the structure of the math.

Example 3: Interpret $3 \times (12 - 4)$ Look at the parentheses first: $(12 - 4)$ is the difference between 12 and 4. The $3 \times$ means we are multiplying that difference by 3. Word Phrase: "Three times the difference of 12 and 4."

Example 4: Interpret $(15 + 5) \div 2$ Inside the parentheses, we have the sum of 15 and 5. Then, we divide that sum by 2. Word Phrase: "The sum of 15 and 5, divided by 2" or "Half the sum of 15 and 5."

The Power of Parentheses

When writing and interpreting expressions, pay close attention to the order of the words. Phrases like "then multiply" or "the sum of" are big clues that you need to use parentheses to group numbers together. Without parentheses, the standard order of operations might change the meaning of your expression completely!