Lessons · Teaching · percent, and the three questions it asks
Percent is a fraction out of a hundred, and it asks three questions
Per cent means per hundred, so 25 per cent is 25/100 is 0.25 is one quarter. Every percent problem is one of three: find the part, find the percent, or find the whole. Knowing which of the three you are in is most of the work.
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In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
A teacher meets percent in a grade book, a reading level, a discount and a test score in the same week, and the three questions look identical on the page. 'Fifteen is what percent of sixty' and 'fifteen per cent of what is sixty' are different questions with very different answers.
How to think about it
Write the relationship as part over whole equals percent over one hundred, then fill in what you know and solve for the gap. That one equation answers all three questions and removes the need to remember three rules.
Worked example
Find the part: 15% of 80 is 0.15 x 80 = 12Percent to decimal, then multiply. The word 'of' is the multiplication.
Find the percent: 12 out of 80 is 12/80 = 0.15 = 15%Part over whole, then turn the decimal into a percent.
Find the whole: 12 is 15% of what? 12 / 0.15 = 80The division that most people reach for multiplication instead.
A 20% discount on 45 leaves 80% of it: 0.80 x 45 = 36One step, not two. Finding the discount and subtracting gives the same 36 the long way.
Your turn
Name the number a percent is always out of.
Per cent means per
Solve one, graded on the server
The trap
Adding and subtracting percents of different wholes. A price that rises 10% and then falls 10% is not back where it started: 100 becomes 110, then 99. The second percent was taken of a bigger number.