Learn
See
Try
Make

Turn a percentage back into counts

What this lesson is about

Every percentage hides two numbers. Find both before you repeat it to anyone.

A district page says eighty per cent of applicants got the scholarship. Your cousin is about to apply on that basis. What first?

Why this matters

A percentage of five people and a percentage of five lakh look the same on a page. Finding the number underneath is the whole work of checking one.

You can turn a percentage back into the two counts behind it, and say when one is missing.

A percentage of five people and a percentage of five lakh look the same on a page. Finding the number underneath is the whole work of checking one.

Behind every percentage sit two counts: the part and the whole.
From 2% to 3% is one point of change, and also one and a half times the old figure.
With the whole missing, say the figure cannot be used yet.

Task

A district page says eighty per cent of applicants got the scholarship.

Weak approach Checking that the state page says eighty per cent too, then writing it as four applicants in five. Neither page gives a count.

Stronger approach Finding the counts first: forty of fifty applicants, in one block, in one year.

Why the stronger approach works Eighty per cent was true and small. The two counts changed what the sentence could be used for.

Try a changed situation A loan agent says the interest went from nine per cent to twelve per cent. He calls that a three per cent rise. What do you write down?

Make something yourself Take three percentages from one page, a scheme page or a news page. For each, write the two counts behind it, or write which of the two is missing.

Lesson 2 of 9 on Reasoning and maths for AI worknextEstimate the answer before you work it outPart 1 ends in a work sample you can send

Read the primary or official source: NCERT · Class 8 Maths, Comparing Quantities