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.