How many percent is that · Lập trình với Martin

Twelve out of sixteen — how many percent is that?

The third and last type of percent question: you know the part and the whole and you ask how many percent the part is. You got 12 right answers out of 16. How many percent of the test is that?

The recipe: divide the part by the whole and multiply by a hundred. So 12 : 16 = 0.75 and 0.75 × 100 = 75%.

Why does it work? By dividing 12 : 16 you find what part of the whole it is (0.75 of the whole, so three quarters). And converting to a percent you already know: times a hundred.

That gives you the full trio of percent questions. Looking for the part? Base times percent. Looking for the base? The ladder via 1%. Looking for the percent? Part over whole, times a hundred. All three questions are just three views of one equation — and from now on, with every word problem you will first decide which of those three numbers is missing.

Tereza and Filip compare English tests. Tereza: 18 marks out of 20. Filip: 21 marks out of 25. “I have more marks, I am better,” Filip reports. Tereza pulls out a pencil: “You cannot compare marks, each test had a different whole.” She counts: 18 : 20 = 0.9, so 90%. Filip: 21 : 25 = 0.84, so 84%. “So I have more marks and a worse result,” Filip frowns. That is exactly why a score is converted to a percent: only the same whole — a hundred — lets you compare fairly.

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Into the division always goes the part first and the whole second: part : whole. If you are not sure of the order, ask: will a number smaller than 1 come out? For a part of a whole it should.

Part over whole, times a hundred

The method:

Step 1: decide what is the whole (what you calculate from — the whole test, the whole price, the whole class) and what is the part.

Step 2: divide the part by the whole. A decimal between 0 and 1 comes out (unless the part grew past the whole).

Step 3: multiply by a hundred and stick on the % sign.

Example: 27 pupils out of 36 went on the trip. 27 : 36 = 0.75 → 75%.

A shortcut via a fraction: simplify 27/36 to 3/4 and the anchor 3/4 = 75% you know by heart. Simplifying often beats a calculator.

When the part grows past the whole, more than 100% comes out. Last year you measured 150 cm, this year 156 cm: 156 : 150 = 1.04 = 104% of last year’s height. That is not a mistake — you are just comparing with a whole that is smaller.

By how many percent vs. how many percent. “How many percent is 156 of 150” → 104%. “By how many percent did you grow” → only the change: 6 : 150 = 0.04 = 4%. The little word “by” means you count the difference, not the whole value.

How many percent is 45 of 60?

Step 1: the whole is 60, the part is 45.

Step 2: I divide: 45 : 60 = 0.75.

Step 3: times a hundred: 75%.

A faster path: I simplify the fraction 45/60 by fifteen to 3/4 and I know the anchor: 75%.

Check with an estimate: 45 is more than a half (30) and less than the whole 60, so the result must sit between 50% and 100%. That checks out.

Of 250 people at a concert, 30 people have a blue T-shirt. How many percent?

Step 1: whole 250, part 30.

Step 2: 30 : 250 = 0.12.

Step 3: 0.12 × 100 = 12%.

Result: 12% of the visitors. Check with the ladder back: 1% of 250 is 2.5 people… sounds odd, but by the numbers: 12 × 2.5 = 30. That checks out. (You can happily calculate percents with “undivisible” things like people — only the result of the part must come out whole in the end.)

The price rose from 400 Kč to 460 Kč. By how many percent did they put the price up?

Watch the little word “by” — I count only the change.

Step 1: the change in price: 460 − 400 = 60 Kč.

Step 2: I divide the change by the original price (that is the whole): 60 : 400 = 0.15.

Step 3: times a hundred: 15%.

Result: they put the price up by 15%. A common mistake is dividing by the new price (60 : 460) — that gives a different, wrong number. The base is always the state before the change.

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With changes always divide by the original value. “By how many percent did they put the price up” is calculated from the price before the rise, not after it. Who divides by the new price gets a smaller percent, and a flyer with a “good” price knows that.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Bắt đầu with ten. When it goes well, add more.

Calculate how many percent a part is of a whole: part divided by whole, times a hundred. Write only the number without %.

Practise the questions

On paper: convert to a hundred

For each question first underline the whole, then calculate. Write the whole method.

How many percent is 21 of 28? Try it also by simplifying the fraction 21/28 to an anchor.
Of 40 shots at the basket Jonáš scored 26. What is his success rate in percent?
The price of a game fell from 800 Kč to 600 Kč. How many percent of the original price is the new price, and by how many percent did the game get cheaper? Two numbers, two different questions.
Invent a test–marks pair so that the success rate comes out exactly 85%, and check by calculating.

Now you 💪

I know the recipe: part divided by whole, times a hundred.
In a question I find the whole and I do not mix it up with the part.
I tell apart “how many percent” (the whole value) and “by how many percent” (only the change from the original value).

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Done when: Four questions xong with the whole underlined; on the third you have two different numbers (75% and 25%) and you can say how the questions differ.

What to take from this lesson

How many percent = part : whole × 100.
Simplifying a fraction to an anchor is often faster than dividing.
Percentages let you compare results with different wholes.
The little word “by” = count only the change, and always from the original value.
The trio of percent questions is complete: part, base, percent.