What Is a Verbal Phrase?

A verbal phrase is a statement or sentence in plain English that describes a mathematical idea. In algebra, it's common to translate these into algebraic expressions to solve problems, represent relationships, or model real-world situations.

Mastering this skill is crucial because word problems, real-life applications, and even higher-level math rely on this translation process.

Tips for Translating Accurately

1. Pay attention to word order.

• “5 less than x” means x−5x - 5x−5, not 5−x5 - x5−x

• “Twice the sum of a number and 4” means 2(x+4)2(x + 4)2(x+4), not 2x+42x + 42x+4

2. Look for grouping words.

• Phrases like “the sum of,” “the difference between,” “the product of,” and “the quotient of” typically suggest parentheses.

3. Know common phrases.

PhraseTranslation“A number”xxx (or any variable)“Twice a number”2x2x2x“A number squared”x2x^2x2“The sum of a number and 7”x+7x + 7x+7“4 less than triple a number”3x−43x - 43x−4

Examples

Example 1:

Phrase: The sum of a number and 6
Translation: x+6x + 6x+6

Example 2:

Phrase: Triple a number, decreased by 2
Translation: 3x−23x - 23x−2

Example 3:

Phrase: The square of a number plus 1
Translation: x2+1x^2 + 1x2+1

Real-World Applications

• Finance: "Interest is 5% of the principal" → 0.05P0.05P0.05P

• Geometry: "The area of a square is the side squared" → A=s2A = s^2A=s2

• Science: "Speed is distance divided by time" → v=dtv = \frac{d}{t}v=td​

Practice Strategy

When translating a phrase:

1. Identify the variable.

2. Determine the operation(s) indicated by keywords.

3. Pay attention to order and grouping.

4. Write a clean expression or equation.