Use the distributive property to expand and evaluate 1/2(1/6 + (-7/6)).
Rewrite with the named strategy, then evaluate exactly.
CCSS 7.NS.A.1d & 7.NS.A.2c · operation strategies
Properties of Operations with Rational Numbers Worksheets
Use properties to make rational-number computation easier instead of merely naming a property from a symbolic template. Problems ask students to pair inverses, pair reciprocals, rewrite subtraction, or distribute before evaluating.
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Properties with Rational Numbers
Properties as strategies · Grade 7 standard · Seed 271701
1.
2.
Use the distributive property to expand and evaluate 3/2(1/4 + 7/4).
Rewrite with the named strategy, then evaluate exactly.
3.
Use commutative and associative properties to evaluate (2 + 4/3) + (-2) by pairing additive inverses.
Rewrite with the named strategy, then evaluate exactly.
4.
Use commutative and associative properties to evaluate (-8/5 × 1) × (-5/8) by pairing reciprocals.
Rewrite with the named strategy, then evaluate exactly.
5.
Use commutative and associative properties to evaluate (-2 + 4/5) + 2 by pairing additive inverses.
Rewrite with the named strategy, then evaluate exactly.
6.
Use commutative and associative properties to evaluate (-1 + 2/3) + 1 by pairing additive inverses.
Rewrite with the named strategy, then evaluate exactly.
7.
Use commutative and associative properties to evaluate (4/3 × 7/4) × 3/4 by pairing reciprocals.
Rewrite with the named strategy, then evaluate exactly.
8.
Use the distributive property to expand and evaluate 2(1/3 + (-4/3)).
Rewrite with the named strategy, then evaluate exactly.
9.
Use commutative and associative properties to evaluate (1/6 × (-1/2)) × 6 by pairing reciprocals.
Rewrite with the named strategy, then evaluate exactly.
10.
Rewrite subtraction as addition of the additive inverse, then solve: 1/3 - (-2/5).
Rewrite with the named strategy, then evaluate exactly.
Exact-construction rule: operations use normalized integer numerator/denominator pairs, number-line positions use exact ticks, repeating decimals come from remainder cycles, and money contexts use exact cents. No answer depends on binary floating-point rounding.
Teaching note 1
Commutative and associative properties can bring additive inverses or reciprocals next to each other.
Teaching note 2
Subtraction can be rewritten as addition of the additive inverse before applying addition strategies.
Teaching note 3
The distributive property should preserve exact rational values on both sides of the rewrite.
Continue the 7.NS progression
Move to another Grade 7 rational-number skill
More skills in this set
Frequently asked questions
Is this only property identification?
No. The prompts use properties as computation strategies and require an evaluated exact result.
Which properties appear?
The set uses commutative, associative, distributive, additive-inverse, and reciprocal reasoning.