Simplification is an important topic in mathematics and quantitative aptitude. It appears in school exams, SSC, banking, railway, police, state government exams, campus placement papers and many entrance tests. A student who understands this topic can solve many questions quickly because the same patterns repeat again and again.
This lesson explains simplification in easy language. It covers meaning, formulas, shortcut ideas, solved examples, exam-style questions, common mistakes, practice questions and FAQs. The explanation is written for beginners, so every method is shown step by step.
Before solving any question, read the complete statement, identify the given values, and write what is required. Then select the formula or method. This habit makes the answer more accurate and saves time in exams.
What Is Simplification?
Simplification means reducing a mathematical expression into its simplest form by applying the correct order of operations and arithmetic rules.
Important Terms
| Point | Details |
|---|---|
| Expression | A combination of numbers and operations |
| BODMAS | Order of brackets, orders, division, multiplication, addition and subtraction |
| Bracket | A symbol used to group operations |
| Fraction | A number written as numerator over denominator |
| Approximation | Finding a near value when exact value is not required |
Important Formulas and Rules
| Point | Details |
|---|---|
| BODMAS order | Bracket, Order, Division, Multiplication, Addition, Subtraction |
| Fraction addition | Take LCM of denominators |
| Decimal operation | Align decimal points |
| Power rule | Solve powers before multiplication |
| Bracket rule | Solve inner brackets first |
Step-by-Step Method
- Remove brackets from inside to outside.
- Solve powers or roots.
- Perform division and multiplication from left to right.
- Perform addition and subtraction from left to right.
- Check signs carefully before final answer.
Shortcut Tricks
- Use cancellation in fractions before multiplication.
- Convert mixed fractions into improper fractions.
- Use decimal to fraction conversion when easier.
- For approximate questions, round numbers sensibly.
- Solve brackets first even if addition looks easier.
Common Question Types
| Point | Details |
|---|---|
| BODMAS expression | Apply operation order |
| Fraction simplification | Use LCM and cancellation |
| Decimal simplification | Convert or align decimals |
| Surd/power expression | Solve powers and roots first |
| Approximation | Use nearest values |
Solved Examples
Example 1
Simplify 20 + 30 ÷ 5.
Division first: 30 ÷ 5 = 6. So 20 + 6 = 26.
Example 2
Simplify (12 + 8) x 3.
Bracket first: 20 x 3 = 60.
Example 3
Simplify 3/4 + 1/2.
LCM is 4. 3/4 + 2/4 = 5/4.
Example 4
Simplify 5² + 10.
Power first: 25 + 10 = 35.
Example 5
Simplify 48 ÷ 6 x 2.
Division and multiplication left to right: 8 x 2 = 16.
Government Exam Style Examples
Question 1
Simplify 36 ÷ 6 + 4 x 3 – 2.
36 ÷ 6 = 6 and 4 x 3 = 12. So 6 + 12 – 2 = 16.
Division and multiplication are done before addition and subtraction.
Question 2
Simplify 2/3 of 45 + 15.
2/3 of 45 = 30. Then 30 + 15 = 45.
The word of usually means multiplication.
Question 3
Simplify 0.5 x 0.4 + 0.2.
0.5 x 0.4 = 0.20. Then 0.20 + 0.2 = 0.4.
Keep decimal places clear.
Common Mistakes
- Solving addition before multiplication.
- Ignoring brackets.
- Changing signs incorrectly.
- Not simplifying fractions before multiplying.
- Doing division and multiplication in wrong left-to-right order.
Practice Questions
- Simplify 10 + 20 ÷ 5.
- Simplify (8 + 12) ÷ 4.
- Simplify 3 x 4 + 5.
- Simplify 7² – 9.
- Simplify 2/5 + 1/10.
- Simplify 0.6 + 0.25.
- Simplify 48 ÷ 8 x 3.
- Simplify 100 – 4 x 12.
- Simplify 3/4 of 80.
- Simplify (5 + 3)².
Answers to Practice Questions
- 14
- 5
- 17
- 40
- 1/2
- 0.85
- 18
- 52
- 60
- 64
Frequently Asked Questions
What is simplification?
It is the process of reducing an expression to a simpler value.
What is BODMAS?
BODMAS gives the correct order of operations.
Which operation comes first?
Brackets and powers come before normal multiplication, division, addition and subtraction.
Is multiplication always before division?
No. Multiplication and division are solved from left to right.
How to improve simplification speed?
Practise cancellation, fractions, decimals and BODMAS regularly.
Revision Notes
Simplification is mainly about order of operations. Follow BODMAS and keep signs clear.
Revise the formulas first, then solve examples without looking at the answer. If your answer is wrong, check whether the mistake was in concept, formula selection, unit conversion or calculation.
Extra Practice Strategy
Start with direct questions and then move to word problems. In the first round, solve slowly and understand every step. In the second round, solve the same type of questions with a timer. This builds both accuracy and speed.
For competitive exams, keep a notebook of common mistakes. Most students lose marks in easy topics because they repeat small mistakes. If you revise your mistakes regularly, your score improves faster.
Conclusion
Simplification becomes easy when the order is followed carefully and calculations are done step by step.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.
Additional Exam Notes
Simplification questions become easier when the condition is converted into a simple mathematical statement. Do not rush to the answer. Write the relation, simplify it, and then calculate. This is especially useful when the question contains ratios, percentages, brackets, ages, signs, fractions or hidden conditions.
Many exam questions are not difficult; they are only written in a tricky way. Read words like more than, less than, after, before, present, twice, half, remaining, total and difference carefully. These words decide the correct equation or operation.
After solving, check the reasonableness of the answer. In ages questions, age cannot be negative. In simplification, bracket order must be followed. In formula questions, the answer should match the unit asked in the question.