Practice Numerical Structure in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The underlying patterns, relationships, and algebraic properties—like commutativity and distributivity—that organize numbers into coherent systems.

Numbers aren't random—they have deep structure (primes, factors, operations).

Example 1

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Identify which properties (commutative, associative, distributive, identity, inverse) are illustrated by each equation: (a) 3 + 5 = 5 + 3, (b) (2 \times 3) \times 4 = 2 \times (3 \times 4), (c) 7(x + 2) = 7x + 14, (d) -8 + 8 = 0.

Example 2

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Use the distributive property to compute 47 \times 98 mentally, and explain the structural reasoning.

Example 3

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Simplify using the appropriate property: (a) (14 + 23) + 37, (b) 6 \times (5 + 9).

Example 4

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Show that \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{a+b}{ab} using the structure of fraction arithmetic, and verify with a=3, b=4.
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