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Number foundations · Topic 1 of 15

Whole Numbers, Place Value & Order of Operations

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Math · whole numbers

Whole Numbers, Place Value & Order of Operations

Place value sets what each digit is worth; PEMDAS sets the order of steps; sign rules decide whether an answer is positive or negative.

01 · Order of operationsPEMDAS: ( ) → exponents → × ÷ → + −
02 · Ties× ÷ tie, + − tie: go left to right
03 · SignsSame signs → +, different signs → −
01

What it is

Each place is worth 10 × the place to its right (ones, tens, hundreds…) must know
Exponent = repeated multiplication of the base: 2⁵ = 2·2·2·2·2 = 32
√n = the positive number that squared gives n: √49 = 7
02

The rules

PEMDAS: Parentheses → Exponents → × and ÷ → + and − must know
× and ÷ are equal, + and − are equal: work each pair left to right must know
× or ÷: same signs → positive; different signs → negative must know
Simplify under the √ first: √(9 + 16) = √25 = 5, not 7
Adding signed numbers: same sign → add; different → subtract, keep larger’s sign
Subtract = add the opposite: 5 − (−3) = 5 + 3 = 8
Order can swap for + and × only (commutative); never for − or ÷
a(b + c) = ab + ac: 4(20 + 3) = 80 + 12 = 92
03

Worked examples

6 + 4 × (5 − 2)² = 6 + 4 × 9 = 6 + 36 = 42
24 ÷ 4 × 2 = 6 × 2 = 12 (left to right, not 24 ÷ 8)
(−6)(−3) ÷ (−2) = 18 ÷ (−2) = −9
04

Signed numbers: adding or multiplying?

Commonly confused
AddMultiply / divide
Same signsAdd the sizes, keep the shared signAnswer is positive
Different signsSubtract the sizes, keep the sign of the largerAnswer is negative
Same-sign example−6 + (−2) = −8(−6) × (−2) = 12
Different-sign example−7 + 4 = −3(−7) × 4 = −28
05

Common mistakes

(−3)² = 9 but −3² = −9 — the exponent hits only its base
06

More detail

Show 4 more facts
Regrouping does not change + or × (associative)
× 0 = 0 and 0 ÷ n = 0, but n ÷ 0 is undefined
Commas split digits into periods of three (ones, thousands, millions)
a + 0 = a and a × 1 = a (identity properties)
Pearl

Please Excuse My Dear Aunt Sally — but × and ÷ tie, and + and − tie: break each tie left to right.

Sources · OpenStax Prealgebra 2e §1.1 Introduction to Whole Numbers · OpenStax Prealgebra 2e §2.1 Use the Language of Algebra · OpenStax Prealgebra 2e §3.2 Add Integers · OpenStax Prealgebra 2e §3.3 Subtract Integers · OpenStax Prealgebra 2e §3.4 Multiply and Divide Integers · OpenStax Prealgebra 2e §5.7 Simplify and Use Square Roots · OpenStax Prealgebra 2e §7.2 Commutative and Associative Properties · OpenStax Prealgebra 2e §7.3 Distributive Property · OpenStax Prealgebra 2e §7.4 Properties of Identity, Inverses, and Zero · Union Test Prep — HESI A2 Mathematics study guide, p. 1: Whole numbers, signed numbers, order of operations · Built from the verified NurseSavvy HESI A2 fact map (facts reviewed 2026-10-16). HESI is a trademark of Elsevier; NurseSavvy is not affiliated with Elsevier.

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