Name the denominator and the requested unit.
Work through shares, original-value changes, reverse percentages and successive changes. Fresh examples separate percentages from percentage points.
Each of six original items contributes one correct answer. The count describes this edition’s fictional quantities and assumptions, not a speed, ability or job-readiness band. All six worked answers and this full guide remain free at every count.
A percentage is relative to a chosen whole
A percent describes a part relative to a base. In these six items, identify whether the base is a collection total, an original value or a newly changed value. Write that base beside the denominator before calculating. The same difference can represent different percentages when divided by different quantities. Neither answer is automatically meaningful without the question. This section reports correct answers about explicit bases; it does not classify you as good or bad with numbers.
An increase uses the original value
A fictional count rising from 250 to 310 increases by 60, so its percentage increase is 60 ÷ 250 × 100 = 24%. The new count is 124% of the original, while the increase is 24%; those are different requested quantities. For a decrease, subtract new from old to obtain the amount lost, then divide by old. A base of zero requires separate handling and does not support ordinary percent-change division; none of these checked items uses it.
Recover the whole from a known share
If 18% of a total is 63, set 0.18 × total = 63. Dividing 63 by 0.18 gives a total of 350. A useful check multiplies 350 by 18% to recover the given 63. Multiplying 63 by 18% at the start would find a part of the part. Label the unknown before deciding whether to multiply or divide, especially when all answer options look numerically plausible.
Successive changes multiply factors
For a fresh quantity of 500, an eight-percent increase followed by a ten-percent decrease gives 500 × 1.08 × 0.90 = 486. The second percentage acts on 540, not on 500. The net change is a decrease of 14, or 2.8% of the original. Adding the signed percentages would predict a two-percent decrease and give the wrong final quantity. Preserve each intermediate base or multiply the factors without rounding early.
Percentage points and relative change answer different questions
A share moving from 18% to 24% rises six percentage points. Its relative increase is separately 6 ÷ 18 × 100, or about 33.3%. Write “points” for the first and “percent of the original share” for the second. Both can describe the same movement, so a bare number invites confusion. For this practice, follow the requested unit exactly and round only when a prompt asks for it; the displayed correct choice reflects that stated rule.
Review the base, not an ability label
For a missed item, mark its part, whole, original and new quantities, then write a one-line equation. Check a new example with the same relationship rather than repeating a memorized number. Six correct counts have no established percentile, speed interpretation, financial-advice meaning or employer threshold. All examples are fictional. A calculator may help arithmetic but cannot choose the correct base for you. Use the worked explanations to inspect that decision, and keep population-level or career conclusions outside this local practice record.