Use algebraic structure
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Use the commutative law to make a friendly pair in 27 + 4 + 3. What is the total?
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Answer: 34
- Reorder the addends: 27 + 3 + 4.
- The first two make 30, so the total is 34. Reordering addition leaves its total unchanged.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Apply number laws and write expressions with clear grouping.
Read the official VCAA curriculum description (VC2M7A02)
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- VC2M7A02-C01Commutative means changing the order of addends or factors. Associative means changing their grouping. For example, (25 × 7) × 4 = (25 × 4) × 7 = 700 uses both laws. They apply to addition and multiplication; subtraction and division cannot generally be reordered or regrouped.
- VC2M7A02-C02A variable stands for a number that can change. “Multiply x by 3, then add 4” is 3x + 4; “add 4 to x, then multiply the result by 3” is 3(x + 4). Distributivity gives 3(x + 4) = 3x + 12 because both terms are multiplied.
- VC2M7A02-C03Track every term and operation when rewriting. A numerical counterexample disproves a claim that two expressions are always equal; one successful substitution does not prove it for all inputs. Explain a valid general rewrite using the appropriate laws.
- VC2M7A02-C04Formulating algebraic expressions and explaining associative, commutative and distributive laws.
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- D01Choose and justify a calculation lawCommutative means changing the order of addends or factors. Associative means changing their grouping. For example, (25 × 7) × 4 = (25 × 4) × 7 = 700 uses both laws. They apply to addition and multiplication; subtraction and division cannot generally be reordered or regrouped.
- D02Translate words and distribute carefullyA variable stands for a number that can change. “Multiply x by 3, then add 4” is 3x + 4; “add 4 to x, then multiply the result by 3” is 3(x + 4). Distributivity gives 3(x + 4) = 3x + 12 because both terms are multiplied.
- D03Test brackets and explain an equivalenceTrack every term and operation when rewriting. A numerical counterexample disproves a claim that two expressions are always equal; one successful substitution does not prove it for all inputs. Explain a valid general rewrite using the appropriate laws.