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J.1 Write numerical expressions for word problems

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What is a numerical expression?

Numerical expressions are math phrases that include numbers and operations, but do not have an equal sign. They show how to calculate a value, but they are not full equations.

Examples:
  • 8 + 6
  • 12 × (3 + 2)
  • (25 − 5) ÷ 4
Note

A numerical expression tells what operations to perform, but it does not show the final answer.

Writing numerical expressions from word problems

To write a numerical expression from a word problem, translate the words into numbers and operations. Look for clues that tell you which operation to use, such as “sum,” “product,” “difference,” or “quotient.”

Example:
  • Word problem: “Add 8 and 6, then multiply the sum by 3.”
  • Expression: (8 + 6) × 3
Note

Always read carefully. The order of operations matters. Use parentheses when an operation must be done first.

Understanding order of operations

The order of operations tells you the correct sequence to solve a numerical expression. This ensures everyone gets the same result.

Order of Operations (PEMDAS):
  • P – Parentheses first
  • E – Exponents (not used often in grade 5)
  • MD – Multiplication and Division (from left to right)
  • AS – Addition and Subtraction (from left to right)
Note

Parentheses help you control the order. Without them, the expression might mean something different.

Examples of word problems and their expressions

Here are examples of how to translate word problems into numerical expressions without solving them:

Examples:
  • “The sum of 12 and 8, divided by 4.” → (12 + 8) ÷ 4
  • “Three times the difference of 20 and 5.” → 3 × (20 − 5)
  • “Add 15 and 9, then subtract 6.” → (15 + 9) − 6
  • “Twice the sum of 10 and 7.” → 2 × (10 + 7)
Note

When you see phrases like “twice,” “more than,” or “less than,” they guide which operation to use and in what order.

Checking your expression

After writing a numerical expression, review the word problem to make sure your expression matches what the problem describes.

Checklist:
  • Did I include all the numbers from the problem?
  • Did I use the correct operations?
  • Did I add parentheses where needed?
Note

Try saying the expression aloud. If it matches the words in the problem, your expression is likely correct.