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).

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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. \(\color{blue}{5x – 10 = 25}\)

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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

How do you translate phrases into an algebraic statement?

Choose a variable for the unknown, then turn each phrase into an operation one piece at a time. ‘Is’ or ‘equals’ becomes =, which turns a phrase into a statement. For ‘eight more than three times a number is 20,’ write 3n + 8 = 20. Then you can solve it: 3n = 12, so n = 4.

How do you translate words into algebraic expressions?

Match key words to operations: sum, more than and increased by mean add; difference, less than and decreased by mean subtract; product and times mean multiply; quotient means divide. So ‘the quotient of a number and 5’ is x/5, and ‘twice a number decreased by 7’ is 2x − 7. Watch the order of words like ‘less than.’

What is the difference between an algebraic expression and an algebraic statement?

An expression is a phrase with numbers, variables and operations but no equal sign, like 4x + 1. A statement, such as an equation or inequality, compares two quantities, like 4x + 1 = 13 or 4x + 1 > 13. In word problems, verbs like ‘is,’ ‘equals’ or ‘is at least’ signal that you are writing a statement, not just an expression.

Is there a translate phrases into an algebraic statement worksheet with answers?

Yes, a free worksheet for translating phrases into algebraic statements is available on Effortless Math, and the answers let you check your work as you go. Try items like ‘six less than a number is 15’ (n − 6 = 15) and ‘the product of 4 and a number is 28’ (4n = 28). Then solve each one to confirm your translation makes sense.

Related Topics

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