Arithmetic Operations – Complete Summary and Review
You have completed the full Arithmetic Operations learning path on MathsFamily. This summary brings together the most important rules, methods, and ideas from every topic so you can review everything in one place.
The Four Operations at a Glance
Operation
Symbol
Meaning
Inverse
Addition
+
Combining amounts
Subtraction
Subtraction
−
Finding a difference
Addition
Multiplication
×
Repeated addition
Division
Division
÷
Sharing or grouping equally
Multiplication
Order of Operations – BODMAS
Letter
Stands for
Example
B
Brackets
(2 + 3)
O
Orders (powers/roots)
4²
D
Division
12 ÷ 4
M
Multiplication
5 × 3
A
Addition
6 + 2
S
Subtraction
9 − 4
Key Rules to Remember
Rule
Example
Commutative (+ and ×)
3+5=5+3; 4×7=7×4
Associative (+ and ×)
(2+3)+4=2+(3+4)
Distributive
3(4+5)=12+15=27
Identity for +
n+0=n
Identity for ×
n×1=n
Zero product
n×0=0
Division by zero
Undefined
Neg × Neg = Pos
(−3)×(−4)=12
Working with Fractions
Operation
Method
Example
Add / Subtract
Same denominator first
1/4+3/4=4/4=1
Multiply
Numerator × numerator; denominator × denominator
2/3 × 3/4=6/12=1/2
Divide
Keep-Change-Flip
2/3 ÷ 4/5 = 2/3 × 5/4=10/12=5/6
Decimal Rules
Add/Subtract: align decimal points; pad with zeros.
Multiply: ignore point; count total decimal places; re-insert.
Divide by decimal: multiply both by power of 10 to remove decimal from divisor.
Powers of 10: move point right to multiply; left to divide.
Checking Your Answers
If you did...
Check by...
Addition
Subtract one addend from the total
Subtraction
Add the difference to the subtrahend
Multiplication
Divide the product by one factor
Division
Multiply the quotient by the divisor
What You Have Learned on This Path
What arithmetic is and why it matters in every area of life.
All four operations with whole numbers, decimals, fractions, mixed numbers, integers, and algebraic expressions.
Mental strategies and shortcuts for fast calculation.
The order of operations and how brackets change results.
Multi-step and word problem strategies.
Arithmetic sequences, mean, ratio, percentage, financial maths, time, units, and science.
Common mistakes to avoid and how to catch errors using inverse operations.
Where to Go Next
You now have a solid foundation in arithmetic. The skills you have built here are the launchpad for every topic ahead — fractions in depth, algebra, geometry, statistics, and beyond. Select a new learning path from the Resources page whenever you are ready.
