Fractions, Decimals & Percentages
Fraction → Decimal
Divide numerator ÷ denominator ¾ = 3 ÷ 4 = 0.75
Decimal → Percent
Multiply by 100 0.75 × 100 = 75%
Percent → Decimal
Divide by 100 75% ÷ 100 = 0.75
% of a number
Multiply: What is 30% of 80? 0.30 × 80 = 24
% change
(New − Old) ÷ Old × 100 Old=50, New=65: (65−50)÷50×100 = 30% increase
% one number is of another
Part ÷ Whole × 100 18 is what % of 72? → 18÷72×100 = 25%
Finding the whole
Part ÷ Rate = Whole 24 is 30% of what? → 24÷0.30 = 80
Ratios & Proportions
Setting up a ratio
Write as a fraction and simplify 15:25 = 15/25 = 3/5
Solving a proportion
Cross-multiply 3/5 = x/20 → 5x = 60 → x = 12
Unit rate
Divide to find rate per 1 $54 for 6 items → $9 per item
Scaling
Multiply/divide both sides equally If 4 officers patrol 8 blocks, 10 officers patrol 20 blocks
Word Problem Setup
- 1. Read the question first: know what you need to find before reading the data.
- 2. Label your unknowns: assign a variable (n, x) to what you're solving for.
- 3. Write the equation: translate words to math ("more than" = +, "of" = ×, "per" = ÷).
- 4. Solve and check units: answer must match what was asked (hours, dollars, people).
- 5. Estimate first: round numbers to verify your exact answer is in the right ballpark.
Common Unit Conversions
Time
60 sec = 1 min
60 min = 1 hr
24 hr = 1 day
7 days = 1 week
Length
12 in = 1 ft
3 ft = 1 yd
5,280 ft = 1 mile
1,760 yd = 1 mile
Weight / Volume
16 oz = 1 lb
2,000 lb = 1 ton
8 fl oz = 1 cup
4 cups = 1 quart
Quick Arithmetic Tips
- ✦ Multiply by 5: Multiply by 10, then halve. (37 × 5 = 370 ÷ 2 = 185)
- ✦ Multiply by 9: Multiply by 10, then subtract the number. (8 × 9 = 80 − 8 = 72)
- ✦ Find 10% quickly: Move decimal one place left. (10% of 340 = 34)
- ✦ Find 5%: Find 10%, then halve. (5% of 340 = 17)
- ✦ Find 15%: Find 10% + 5%. (15% of 340 = 34 + 17 = 51)
- ✦ Divisibility by 3: Sum of digits divisible by 3. (123: 1+2+3=6 ✓)
- ✦ Practice without a calculator first: many civil service exams limit outside devices, so build comfort doing the work by hand unless your exam notice says otherwise.
More free study sheets
Other reference sheets that apply to every civil service exam.
Reading Comprehension Strategy Sheet
A structured one-page guide to common question types on civil service reading passages and practical ways to approach them. Includes common traps and how to avoid them.
View & print →Exam Day Checklist
A practical checklist for what to confirm before, during, and after your civil service exam. Always compare it with your official exam notice because agency rules can differ.
View & print →Situational Judgment Test (SJT) Cheat Sheet
The SJT is the section many test-takers underestimate. This sheet explains common response patterns, workplace dimensions often evaluated, and a framework for choosing the strongest answer.
View & print →Which exam are you preparing for?
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