Five Minutes: Check a Percentage Denominator

Learning objective

Explain what a percentage is a percentage of, and calculate it from a stated count.

Your five-minute route

Allow about one minute for the idea, one minute for the worked example, two minutes for your own answer and one minute for feedback. Work at your own pace. These timings are estimates. Use a notebook or a document for your response; no answer is submitted and no account progress is recorded.

One useful idea

For a count-based percentage, divide the selected count by the relevant total and multiply by 100. The denominator is that total. Name the group, period and eligibility rule. A correct calculation can still answer the wrong question if the total represents a different group. Do not calculate a percentage with a zero denominator.

Worked example

A fictional session has 60 bookings and 40 attendees. Twelve attendees complete an exercise. Among attendees, completion is 12 divided by 40, multiplied by 100: 30%. Among all bookings, it is 12 divided by 60, multiplied by 100: 20%. Both calculations are arithmetically correct, but they answer different questions. Neither establishes why someone did not attend or complete.

Check your learning

A fictional workshop has 32 attendees. Eight submit feedback. Calculate the percentage of attendees submitting feedback and write a clear sentence. What should you report for a different workshop with no attendees, rather than inventing a feedback percentage? Write your answer before reading the explanation below.

Answer and explanation

Eight divided by 32, multiplied by 100, equals 25%. A clear statement is: “Eight of the 32 attendees submitted feedback for this workshop, a response rate of 25%.” For a workshop with no attendees, the attendee-based rate is not calculable because the denominator is zero. Record the zero count and use a clearly defined “not applicable” or missing-rate status; do not label the rate 0% without a valid denominator.

Use it in your work

Before sharing a percentage, write its numerator and denominator in words. Check that the selected count belongs to the stated total and that records use the same period. Explain any exclusions. Keep the original counts so a reviewer can reproduce the calculation.

Completion check

You have completed this unit when you can explain the idea in your own words, compare your answer with the explanation and apply the same approach to one new example. If your answer missed a key point, revise it and try again. This is a practice lesson, not an examination or a validated assessment.

Sources and provenance

The arithmetic and examples are original RDE practice material. All numbers are fictional. For presentation conventions, see Office for National Statistics: Percentages and percentage points. The scenarios and answer explanations are original RDE teaching examples. Names, organisations and records used in examples are fictional. Reviewed 8 October 2026. Author: Jefferson Otonbara Imgbi.

Cover image: AI-generated illustrative scene created specifically for this resource.