Syllabus mapping
A foundation for the rest of arithmetic
SSC’s indicative Mathematical Abilities syllabus includes decimals, fractions and relationships between numbers. These skills return in percentage, ratio, average, profit and loss, interest, time and work, mixtures and data interpretation.
Concept 1
What a fraction represents
In a/b, the numerator a counts equal parts and the denominator b names their size. The denominator cannot be zero. The notation also means a ÷ b.
Proper
Numerator smaller than denominator: 3/8. A positive proper fraction lies between 0 and 1.
Improper
Numerator at least the denominator: 11/4. Its value is at least 1.
Mixed
2 3/4 = (2×4+3)/4 = 11/4. Convert before multiplying or dividing.
Equivalent fractions: multiply or divide numerator and denominator by the same non-zero number: 3/5 = 6/10 = 21/35.
Concept 2
Reduce and compare
Divide numerator and denominator by their HCF. Thus 84/126 = 2/3.
| Situation | Method | Example |
|---|---|---|
| Same denominator | Compare numerators | 7/12 > 5/12 |
| Same positive numerator | Smaller denominator is larger | 5/8 > 5/11 |
| Different denominators | Cross-multiply | 7/12 vs 5/8: 56 < 60, so 5/8 is larger |
| Both near 1 | Compare missing parts | 11/12 > 7/8 because 1/12 < 1/8 |
Concept 3
The four fraction operations
Add or subtract
Use a common denominator: 3/8+5/12=9/24+10/24=19/24.
Multiply
Cancel common factors first: (14/15)×(25/28)=5/6.
Divide
Multiply by the divisor’s reciprocal: (7/12)÷(14/9)=3/8.
Order: brackets, powers, division and multiplication left to right, then addition and subtraction left to right. A fraction bar groups its entire numerator and denominator.
Concept 4
Decimal place value
| Decimal | Meaning | Fraction |
|---|---|---|
| 0.7 | 7 tenths | 7/10 |
| 0.42 | 42 hundredths | 21/50 |
| 0.375 | 375 thousandths | 3/8 |
- For addition or subtraction, align decimal points.
- For multiplication, multiply as integers and restore the total decimal places.
- Multiplying by 10, 100 or 1000 moves the point right; dividing moves it left.
- Estimate first: 19.8×0.49 is near 10, so 0.97 and 97 are impossible.
Concept 5
Convert without changing value
Terminating decimal to fraction
Use a power of 10 and reduce: 2.375=2375/1000=19/8.
Fraction to decimal
Divide numerator by denominator or create a power-of-ten denominator: 3/8=375/1000=0.375.
Recurring decimal
Let x=0.272727…. Then 100x=27.272727…. Subtract: 99x=27, so x=3/11. If x=0.1666…, then 100x−10x=15, so x=1/6.
Useful exact values: 1/2=.5; 1/4=.25; 3/4=.75; 1/5=.2; 1/8=.125; 3/8=.375; 5/8=.625; 7/8=.875.
Concept 6
Will the decimal terminate?
Reduce the fraction first. Its decimal terminates exactly when the denominator has no prime factor except 2 or 5.
| Lowest form | Denominator | Result |
|---|---|---|
| 7/40 | 2³×5 | Terminates: .175 |
| 11/24 | 2³×3 | Recurring |
| 21/75=7/25 | 5² | Terminates: .28 |
| 13/30 | 2×3×5 | Recurring |
Reduce first: 6/15 becomes 2/5 and therefore terminates.
Worked methods
Examples with reasoning
Compare 17/24 and 23/32
17×32=544 and 23×24=552, so 23/32 is larger.
Evaluate 2 1/3−5/6
7/3−5/6=14/6−5/6=9/6=3/2=1 1/2.
Evaluate 1.25×0.48
125×48=6000; restore four decimal places to obtain .6000=.6.
Find 3/5 of 2 1/4
“Of” means multiply: (3/5)×(9/4)=27/20=1.35.
Exam traps
Errors that cost marks
Adding denominators
2/7+3/7=5/7, not 5/14.
Wrong reciprocal
Invert only the divisor during division.
Comparing numerators
Different denominators require a valid comparison method.
Ignoring place value
0.8=0.80, so it is greater than 0.79.
Skipping reduction
Reduce before applying the termination test.
No estimate
Check the scale before accepting a decimal answer.
Original practice
Check understanding after learning
Original syllabus-aligned questions—not claimed previous-year questions.
Rapid revision
The one-minute sheet
- Reduce by the HCF; equivalent fractions preserve value.
- Use a common denominator for addition and subtraction.
- Cancel before multiplying; use the reciprocal when dividing.
- Align decimal points and estimate the scale.
- A reduced denominator containing only 2s and 5s terminates.
- Use algebraic shifting and subtraction for recurring decimals.
Source and authorship ledger
Official syllabus and learning foundations
- SSC CGL indicative Mathematical Abilities syllabus
- SSC CHSL indicative Mathematical Abilities syllabus
- NCERT official mathematics exemplar directory
- NCERT learning outcomes for fractions and decimals
Explanations, tables, examples and questions are original course material. NCERT resources are credited references and are not reproduced. Reviewed 24 September 2026.
Percentages: conversions, change, successive effects and applications.