Key word operators

Converting words to numbers

This chapter focuses on converting words into numbers. That means taking a word problem and rewriting it in numerical terms (an equation). This skill is essential for solving word problems because the wording and details can lead to mistakes even when you understand the math. In this chapter, you’ll practice spotting key words and translating them into mathematical operations.

The following list shows common mathematical operators and the words that often signal them in word problems:

Most of this chapter is practice applying these terms. In the examples below, you’ll be given a word problem and asked to turn it into an equation. It’s most helpful to try each one yourself before revealing the answer.

Practice: Rewrite the following problems as equations

Example 1

We’ll do the first one together:

A number is three less than four times a second number.

• “A number” is an unknown value, so we’ll represent it with a variable. Use $x$.
• “Is” translates to $=$.
• “Three less than” means subtract $3$.
• “Four times” means multiply by $4$.
• “A second number” is a different unknown, so use a new variable, $y$.

Writing it as an equation:

$x=4\ast y-3$

Example 2

$5$ times the original number is $2$ more than the new number.

Example 3

A second book is worth four more than two out of seven of the original book.

Example 4

When a car is driven off its dealership parking lot, its value becomes half its original value

Example 5

There is an apartment in town that charges $\$400$ as a down payment and $\$600$ more for each month rented out. How much would it cost to rent the apartment for $6$ months?