Arithmetic & Order of Operations Master Hub
From column operations to long division, PEMDAS priority rules, and signed integers.
PDF + Answer KeysArithmetic & PEMDAS 50-Worksheet Master Workbook
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The 5-Stage Arithmetic & PEMDAS Roadmap
Addition, Subtraction & Regrouping
Build core computation fluency with vertical column alignment, carrying, borrowing, and word problems.
Multi-Digit Addition (with Carrying / Regrouping)
Align numbers by place value and master carrying across 2-digit, 3-digit, and 4-digit addition columns.
Multi-Digit Subtraction (with Borrowing)
Master borrowing from tens and hundreds place values when the top digit is smaller than the bottom digit.
Math Word Problems & Place Value Expansion
Translate real-world word problems into arithmetic equations and master base-10 expanded form.
Times Tables & Multi-Digit Multiplication
Progress from instant single-digit times tables recall to 2-digit by 2-digit multi-digit partial products.
Times Tables Mastery (1 to 12 Multiplication Facts)
Develop rapid mental math fact recall with structured visual multiplication tracks and timed drills.
Multi-Digit Long Multiplication (Standard Algorithm)
Master column multiplication: multiply partial products, add the placeholder zero, and sum the columns.
Number Patterns & Arithmetic Sequences
Identify linear stepping rules, missing number terms, and pattern recognition algorithms.
Division with Remainders (DMSB Cycle)
Master Euclidean division with 1-digit and 2-digit divisors using the proven Dad-Mom-Sister-Brother cycle.
Long Division Step-by-Step (with Remainders)
Follow the 4-step DMSB cycle: Divide, Multiply, Subtract, Bring Down with quotient and remainder checks.
Division Facts & Single-Digit Divisors
Understand division as the inverse of multiplication with equal sharing and group grouping models.
Order of Operations (PEMDAS) & Signed Integers
Apply strict operational hierarchy (Parentheses, Exponents, Mult/Div, Add/Sub) and compute with negative numbers.
Order of Operations (PEMDAS / BODMAS)
Evaluate multi-step expressions without falling into the left-to-right trap. Parentheses ➔ Exponents ➔ MD ➔ AS.
Adding & Subtracting Signed Integers (Negative Numbers)
Master number line jumps and the "minus a minus becomes a plus" rule using the hot air balloon mental model.
Multiplying & Dividing Signed Integers
Learn the sign multiplication matrix: same signs yield positive (+), different signs yield negative (−).
Factors, Multiples, Roots & Percentages
Explore foundational number theory: Prime factorization, GCD/LCM, square roots, cube roots, and percentages.
Greatest Common Divisor (GCD) & LCM
Find common factors and lowest common multiples for simplifying fractions and solving cycle word problems.
Square Roots (√x), Cube Roots (∛x) & Factorials (n!)
Calculate perfect square roots, cubic dimensions, and factorial permutations with step-by-step breakdowns.
Percentage Increase, Decrease & Discounts
Calculate percentage markups, tax, sale discounts, and relative percentage change with clear formulas.
Ratios, Proportions & Cross-Multiplication
Master recipe scaling, unit rates, part-to-part vs part-to-whole sharing, and the cross-multiplication butterfly method.
Frequently Asked Questions
Everything teachers, homeschoolers, and students need to know about elementary and middle school arithmetic.
What is the correct order of operations in math (PEMDAS / BODMAS)?
The order of operations is: 1) Parentheses / Brackets, 2) Exponents / Orders, 3) Multiplication and Division (evaluated from left to right), and 4) Addition and Subtraction (evaluated from left to right).
What are the 4 steps of long division (DMSB)?
The 4 steps are: 1) Divide the current digit by the divisor, 2) Multiply the result by the divisor, 3) Subtract that product from the current number, and 4) Bring Down the next digit. Repeat until all digits are brought down.
What is the rule for multiplying negative integers?
When multiplying two numbers with the SAME sign (two positives or two negatives), the answer is always POSITIVE. When multiplying two numbers with DIFFERENT signs (one positive and one negative), the answer is always NEGATIVE.
Are all PanMaths arithmetic worksheets printable with answer keys?
Yes! Every arithmetic worksheet generator on PanMaths produces clean, ink-efficient printable PDF worksheets complete with step-by-step worked answer keys for teachers, classrooms, and homeschoolers.