4.1 Arithmetic, Percentages, and Ratios
Key Takeaways
- Mathematics is a common civil-service basic skills domain, but the exact weight depends on the hiring notice; this practice blueprint uses 20% for balanced coverage.
- Accurate arithmetic starts with labels: total, part, rate, unit price, difference, and remaining quantity should be identified before calculating.
- Percent questions usually use one of three setups: part = percent x whole, percent = part divided by whole, or percent change = change divided by original.
- Ratio questions require deciding whether the question asks for part-to-part or part-to-whole, then converting the ratio into total parts when needed.
- A useful math error log records the wrong setup, the corrected setup, and one prevention rule for the next timed drill.
Why This Topic Matters
Civil service basic skills exams use arithmetic because government offices use arithmetic. A clerk may total fees, a dispatcher may compare staffing levels, a benefits assistant may check a payment adjustment, and a warehouse aide may verify whether enough supplies remain. The numbers are usually friendly; the challenge is selecting the correct relationship under time pressure.
The exact math weight is controlled by the agency or jurisdiction notice. This guide follows a balanced 20% mathematics blueprint for practice, so use it to build skill while still checking the announcement for your target position.
Arithmetic Setup First
Before calculating, write a short label for each number. The most common wrong answers come from using the correct operation on the wrong quantity, such as applying a discount to the final price instead of the original price, or dividing by the number of days when the question asks for the number of workers.
| What the question asks | Setup signal | First line to write |
|---|---|---|
| Total amount | combined, altogether, in all | add matching units |
| Difference | more than, fewer than, remaining | subtract from the larger or original amount |
| Repeated groups | each, per item, every | multiply count by amount per item |
| Equal share | each group, average, per one | divide total by number of groups |
Worked Example: Supply Cost
A department buys 16 clipboards at $6 each and 24 badge holders at $3 each. The clean setup is clipboard cost = 16 x 6 = 96 and holder cost = 24 x 3 = 72. The order total is 96 + 72 = $168. Writing the two subtotals prevents the common error of multiplying 16 by 3 or 24 by 6.
Percent Toolbox
A percent is a rate per 100. Convert it to a decimal when the arithmetic is direct: 18% becomes 0.18, 7.5% becomes 0.075, and 120% becomes 1.20. For mental math, use anchor percents: 10% is one-tenth, 5% is half of 10%, 1% is one-hundredth, 25% is one-fourth, and 12.5% is one-eighth.
| Percent task | Reliable setup | Check question |
|---|---|---|
| Find a percent of a whole | part = percent x whole | What amount is represented? |
| Find what percent one number is | percent = part divided by whole | Which number is the original whole? |
| Find percent increase or decrease | change divided by original | Did the question ask old-to-new or new-to-old? |
| Apply markup or discount | original plus or minus change | Is the final price requested? |
Worked Example: Percent Change
A permit counter handled 320 visits last week and 368 visits this week. The increase is 368 - 320 = 48 visits. Percent increase uses the original amount as the base, so 48 divided by 320 = 0.15, or 15%. A wrong setup of 48 divided by 368 would compare the change with the new amount, not the original workload.
Ratios and Proportions
A ratio compares quantities in a fixed relationship. The first decision is whether it is part-to-part or part-to-whole. If the ratio of inspectors to clerks is 2:7, there are 2 inspector parts, 7 clerk parts, and 9 total parts. A question about the whole group requires the total parts, not just one side of the ratio.
Worked Example: Staffing Ratio
A records unit keeps a 3:5 ratio of morning staff to afternoon staff. If the full daily staff is 48 people, the ratio has 8 total parts. One part is 48 divided by 8 = 6 people. Morning staff is 3 x 6 = 18 and afternoon staff is 5 x 6 = 30.
Error-Log Guidance
After practice, classify each miss by cause, not by topic alone. Useful categories are reading error, operation choice, arithmetic slip, percent-base error, ratio relationship error, and unit error. For each missed item, copy only the corrected setup line and add one prevention rule, such as "identify the original amount before percent change" or "add ratio parts before solving whole-group questions."
A good log turns one miss into a repeatable habit. If three entries say percent-base error, do not do another mixed set yet. Spend ten minutes drilling original-whole identification, then return to timed practice.
Final Accuracy Check
Before selecting an answer, ask whether the answer is in the requested unit, whether the size is reasonable, and whether you answered the exact relationship. A ratio of blue forms to all forms is not the same as blue forms to green forms. A 20% increase is not the same as adding 20. These quick checks catch many civil-service math traps.
A licensing office orders 14 receipt books at $8 each and 18 stamp pads at $5 each. What is the total cost of the order?
A unit completed 420 requests in April and 462 requests in May. What was the percent increase from April to May?
The ratio of temporary employees to permanent employees in a project office is 1:4. If the office has 35 employees in all, how many are temporary employees?