Civil Service Math Quick Reference — Free Printable

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

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

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.

Key word translations:

sum → +difference → −product → ×quotient → ÷is / was → =of → ×more than → +less than → −per → ÷total → +times → ×split equally → ÷

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

✦ 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 ✓)
✦ No calculator allowed — practice pencil-and-paper until these are automatic.

Practice what you've reviewed

Take our free 60-question civil service practice test.