Numerical Structure Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Simplify using the appropriate property: (a)

(14 + 23) + 37

, (b)

6 \times (5 + 9)

1
(a) Use associativity: $(14 + 23) + 37 = 14 + (23 + 37) = 14 + 60 = 74$ .
2
(b) Use distributivity: $6 \times (5 + 9) = 6 \times 5 + 6 \times 9 = 30 + 54 = 84$ .

Answer

(a)

74

; (b)

84

Choosing the right property can simplify arithmetic dramatically. Re-associating to group

23 + 37 = 60

in (a) avoids an awkward intermediate step. Distributing in (b) breaks one two-digit multiplication into two single-digit ones.

About Numerical Structure

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

Identify which properties (commutative, associative, distributive, identity, inverse) are illustrate

Use the distributive property to compute [formula] mentally, and explain the structural reasoning.

Show that [formula] using the structure of fraction arithmetic, and verify with [formula], [formula]