What Are Percentages?
Percent means per hundred. Once a child hears the word that way, most percentage questions stop being a new topic and become a fraction they already know.
Percent means per hundred
A percentage is a fraction with 100 on the bottom.
The word does the explaining. "Per cent" means "per hundred", from the same root as century and cent. So 35 percent means 35 out of every 100.
That is why 35100 and 35% and 0.35 are three ways of writing one amount. Nothing is being converted, only renamed.
The hundred square
A grid of 100 small squares makes this literal. Shade some of them and you have shaded a percentage.
Count in blocks of five using the heavier grid lines. Counting one square at a time is where children lose patience with this topic.
The percentage bar
Grids are good for showing what a percentage is. Bars are better for comparing them.
Worth knowing by heart
These come up constantly. A child who knows them stops calculating and starts thinking.
- 50% is a half
- 25% is a quarter, and 75% is three quarters
- 10% is a tenth, which is the most useful one of all
- 20% is a fifth
- 1% is a hundredth
- 100% is all of it, and 0% is none of it
Above one hundred
Children often assume 100% is a maximum. It is not, and saying so early prevents confusion later.
100% means all of one thing. If something doubles, it becomes 200% of what it was. Prices rise by 150%. A business grows 300%. None of that is a mistake.
When 100% really is the limit
It depends on what is being measured. You cannot eat 120% of a cake, because the cake runs out. You can absolutely earn 120% of last year's salary. The percentage is not the limit, the thing it describes is.
Common mistakes
1. Forgetting what the whole is
Comparing 20% of a small class with 20% of a large one as if they were the same number of children. A percentage is always a percentage OF something. Ask "of what?" before doing anything else.
2. Reading the percent sign as a decimal point
Treating 5% as 5.0 or as 0.5. Five percent is 5 out of 100, so as a decimal it is 0.05. Say the words "five per hundred" out loud and the decimal follows on its own.
3. Adding percentages of different wholes
Scoring 80% on a short test and 60% on a long one, then calling the average 70%. It is only 70% if both tests were worth the same. Percentages of different wholes cannot simply be averaged.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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For parents
Say "per hundred" instead of "percent" for a week, out loud, every time it comes up. "Thirty per hundred off." It sounds odd for about two days and then the whole topic stops being abstract, because the child is hearing the definition every single time.
What to learn next
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