Why you do not end up where you started
| 10% of 200 | = 20 |
| 10% of 350 | = 35 |
| 20% of 200 | = 40 |
| 5% of 200 | = 10 |
divided by ten
moved the digits
Both work. One is faster when the numbers stop being round.
Do not compute. Predict.
That is the answer almost every adult gives. In fifteen minutes you will know whether it is right — I am not going to tell you.
Twenty per cent of what? Of ₱100.
The shirt costs ₱120 right now. That is what the second 20% is taken of.
Why?
The second amount is always bigger — because the base grew.
| 15% of what, first? | of ₱800 → ₱120 → ₱680 |
| Now up 15%. Of what? | of ₱680 → ₱102 → ₱782 |
Down first, and we still finish below ₱800.
₱800 → ₱680 → ₱782
₱800 → ₱920 → ₱782
The same. Remember that — it is tomorrow's lesson.
| Start | Change | Then | The two amounts | Result |
|---|---|---|---|---|
| ₱100 | up 20% | down 20% | ₱20 · ₱24 | ₱96 |
| ₱500 | up 10% | down 10% | ₱50 · ₱55 | ₱495 |
| ₱1 200 | up 25% | down 25% | ₱300 · ₱375 | ₱1 125 |
| ₱800 | down 15% | up 15% | ₱120 · ₱102 | ₱782 |
| ₱240 | up 50% | down 50% | ₱120 · ₱180 | ₱180 |
“That percentage — of what?”
↓ crossed out by someone who voted for it
A quarter of the value, gone. Bigger percentage, bigger loss.
You did two calculations for every row today. There is a way to do each row in one.
Quarter sheet. Name at the top. Question 3 is the one that counts.