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Grade 5 · lesson 1 of 4

Evaluate Expressions with Grouping Symbols

Identify and calculate the parenthesized part.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: For 4×(6+3), the group is nine, so the result is 36.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Parentheses specify which part of an expression is treated as one grouped quantity. Evaluate that part first, then multiplication or division, then addition or subtraction in conventional order. A different grouping can change the result even when all the written numbers and operation symbols are the same.

Identify and calculate the parenthesized part. Substitute its value into the remaining expression and continue in operation order. Compare the ungrouped version to explain why a supplied pair may produce different answers.

Treat the grouped sum as one quantity. Do not ignore parentheses when multiplying a sum. Draw a box around each grouped quantity before calculating.

  1. Draw a box around each grouped quantity before calculating.
  2. Follow the worked example. Point to each number or shape feature and say what it tells you.
  3. Identify and calculate the parenthesized part.
  4. Try the question and then the three practice questions. Check your answers and explain any change you make.
Worked example

See the method in action

For 4×(6+3), the group is nine, so the result is 36. Without parentheses, 4×6+3=24+3=27. The grouped expression multiplies the whole sum by four, while the ungrouped version multiplies only six and then adds three. Treat the grouped sum as one quantity. Do not ignore parentheses when multiplying a sum. Draw a box around each grouped quantity before calculating.

Your turn

Check your reasoning

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Helpful tips
  • Treat the grouped sum as one quantity.
  • Do not ignore parentheses when multiplying a sum.
Evaluate 3×(4+5).

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

27

Calculate the grouped sum before multiplying. The result is 27.

Take it further

Evaluate (18−6)÷3 and 18−6÷3. Expected: 4 and 16.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Evaluate 3×(5+5).
Need a hint?
  • Treat the grouped sum as one quantity.
  • Do not ignore parentheses when multiplying a sum.
2. Evaluate 3×(6+5).
Need a hint?
  • Treat the grouped sum as one quantity.
  • Do not ignore parentheses when multiplying a sum.
3. Evaluate 3×(7+5).
Need a hint?
  • Treat the grouped sum as one quantity.
  • Do not ignore parentheses when multiplying a sum.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.