Math Drills

Commutative, Associative, and Distributive Laws

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What this worksheet covers

Grade: Grade 4 (Elementary School)
Topic: Rules of Calculation
Worksheet: Commutative, Associative, and Distributive Laws

The expression is regrouped before any answer is found. Chain of Addition (Commutative and Associative) and Chain of Multiplication (Commutative and Associative) clear away the pairs that gather neatly, while Parentheses in Addition and Subtraction (Associative Law) and Parentheses in Multiplication and Division (Associative Law) redraw where the parentheses cut. Taking out a shared figure, splitting a number close to 100, and a word problem about cost follow.

Commutative Law, Multiplication (Fill in the Blank), which merely swaps the order of the factors, is settled by copying a figure across, and the addition side carries the same shape. Round Numbers, Addition (Fill in the Blank), which moves the amount that made a figure round, and Doubling, Halving, Multiplication (Fill in the Blank), which doubles one side and halves the other to make ten or a hundred, leave the regrouping motionless if the box keeps the original figure.

In Expressions Using a Box a scene is turned into an expression with the unknown place left as a box. What is gained here is the judgement that the order settled in Order of Operations with Whole Numbers may be shifted so long as the answer does not move.