How to Translate Phrases into an Algebraic Statement? (+FREE Worksheet!)

One of the most important skills in Algebra 1 is the ability to translate phrases into an algebraic statement. Word problems, real-world applications, and standardized tests all require you to convert ordinary language into mathematical expressions and equations. This lesson gives you the keyword tables, worked examples, and practice you need to master this skill.

What Is Translating Phrases into an Algebraic Statement?

Translating phrases into an algebraic statement means replacing words with math symbols. A variable (usually x, y, or n) stands for the unknown quantity, and operation keywords tell you which symbol to use. The result can be an expression (no equals sign) or an equation (with an equals sign).

Algebra I for Beginners 2026 The Ultimate Step by Step Guide to Acing Algebra I

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Operation Keywords Reference

Addition Keywords

sum, plus, increased by, more than, added to, total of, combined

• “5 more than a number” → \(\color{blue}{x + 5}\)
• “the sum of a number and 9” → \(\color{blue}{n + 9}\)

Subtraction Keywords

difference, minus, decreased by, less than, subtracted from, fewer than, reduced by

• “a number decreased by 4” → \(\color{blue}{x – 4}\)
• “8 less than a number” → \(\color{blue}{x – 8}\)  (note: “less than” reverses the order)

Multiplication Keywords

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

• “three times a number” → \(\color{blue}{3x}\)
• “twice the sum of a number and 7” → \(\color{blue}{2(x + 7)}\)

Division Keywords

quotient, divided by, per, ratio of, split into

• “a number divided by 6” → \(\color{blue}{x \div 6}\) or \(\color{blue}{\frac{x}{6}}\)
• “the quotient of 15 and a number” → \(\color{blue}{15 \div n}\)

Equals Keywords (forming equations)

is, equals, is equal to, gives, yields, results in

• “a number plus 3 is 10” → \(\color{blue}{x + 3 = 10}\)

Step-by-Step Summary

1. Read the phrase carefully and identify the unknown — assign it a variable.
2. Locate the operation keyword and choose the correct symbol.
3. Watch for reversed-order phrases like “less than” and “subtracted from.”
4. Look for an equals keyword to decide whether you have an expression or an equation.
5. Write the algebraic statement in the correct order.

Watch: Translating Words into Algebraic Expressions

The Organic Chemistry Tutor explains the keyword approach with clear, worked examples:

Translate Phrases into an Algebraic Statement – Worked Examples

Example 1: “The product of a number and 7, decreased by 4.”

Product → multiplication; decreased by → subtraction.
\(\color{blue}{7x – 4}\)

Example 2: “Six less than twice a number equals 14.”

Twice a number → \(\color{blue}{2x}\); six less than → subtract 6 from that; equals → =.
\(\color{blue}{2x – 6 = 14}\)

Example 3: “The quotient of a number and 5 is 3 more than the number.”

Quotient of n and 5 → \(\color{blue}{\frac{n}{5}}\); 3 more than the number → \(\color{blue}{n + 3}\); is → =.
\(\color{blue}{\frac{n}{5} = n + 3}\)

Example 4: “Four times the sum of a number and 9.”

Sum of a number and 9 → \(\color{blue}{(x + 9)}\); four times → multiply by 4.
\(\color{blue}{4(x + 9)}\)

More Practice: Video with Additional Examples

Mashup Math provides more translation examples with real-word problems:

Exercises: Translate Phrases into an Algebraic Statement

Write an algebraic expression or equation for each phrase.

1. A number increased by 11.
2. Three times a number minus 8.
3. The sum of a number and 5 equals 20.
4. Twice a number increased by 7 is 19.
5. The quotient of a number and 4, plus 2.
6. Ten less than five times a number equals 25.

Answers

1. \(\color{blue}{x + 11}\)
2. \(\color{blue}{3x – 8}\)
3. \(\color{blue}{x + 5 = 20}\)
4. \(\color{blue}{2x + 7 = 19}\)
5. \(\color{blue}{\frac{x}{4} + 2}\)
6. \(\color{blue}{5x – 10 = 25}\)

Pre-Algebra Exercise Book A Comprehensive Workbook + PreAlgebra Practice Tests

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.

Want More Practice?

We haven’t published a worksheet built specifically for Translate Phrases into an Algebraic Statement just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work — they’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Variables Expressions and Properties Worksheet
• Download Introduction to Equations and Solutions Worksheet
• Download Simplifying Algebraic Expressions Worksheet

Frequently Asked Questions

What does “less than” mean in algebra?

“Less than” reverses the order of the terms. “8 less than a number” means \(\color{blue}{x – 8}\), not \(\color{blue}{8 – x}\).

How do I know when to write an equation vs. an expression?

Look for an equals keyword such as is, equals, or results in. If that word appears, write an equation (with =). If not, the result is just an expression.

Can one phrase have more than one operation?

Yes. “Twice the sum of a number and 3” involves both multiplication and addition: \(\color{blue}{2(x + 3)}\). Use parentheses whenever a sum or difference is multiplied or divided as a unit.

Related Topics

• Order of Operations
• The Distributive Property
• Multiplying and Dividing Integers
• Percent Problems
• Simple Interest