Translate Words Into Algebraic Expressions

Translate Words Into Algebraic Expressions

When you turn words into an algebraic expression, the goal is to replace the unknown quantity with a variable and keep the mathematical relationships the words describe.

1) Identify the unknown

Choose a letter for the number you do not know. For example, let (x) represent the unknown quantity.

2) Look for operation words

Match common phrases to operations:

• sum, plus, increased by → add
• difference, minus, less than → subtract
• product, times, multiplied by → multiply
• quotient, divided by → divide

Be careful with word order. For example, “5 less than (x)” means (x - 5), not (5 - x).

3) Write the expression clearly

Convert each part of the phrase into symbols. If the phrase includes a number and a variable, place them in the correct order and use parentheses when needed.

4) Simplify if possible

If the expression contains like terms or obvious arithmetic, simplify the result. For example, (3x + 2x = 5x).

5) Check your translation

Read the expression back in words and make sure it matches the original phrase. This helps catch reversed order or missing operations.

A good habit is to translate one piece at a time, then verify that the final expression says exactly what the words say.