Up 20%,
Down 20%

Why you do not end up where you started

Week 7 · Day 1 CG Quarter 1 · competency 7 45 minutes

Four quick ones

10% of 200= 20
10% of 350= 35
20% of 200= 40
5% of 200= 10
How did you find 10%?
Some of you

divided by ten

Some of you

moved the digits

Both work. One is faster when the numbers stop being round.

A shirt costs ₱100.
The price goes UP 20%.
Then the price goes DOWN 20%.
What does it cost now?

Do not compute. Predict.

Hands up. Count them.

back to ₱100
__
more
__
less
__
Say this, and mean it

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.

First: UP

UP
20% of ₱100 = ₱20
₱100 + ₱20 = ₱120
DOWN
20% of ₱ ?

Twenty per cent of what? Of ₱100.

Now: DOWN. Twenty per cent of what?

UP
20% of ₱100 = ₱20
₱100 + ₱20 = ₱120
DOWN
20% of ₱120 = ₱24
₱120 − ₱24 = ₱96

The shirt costs ₱120 right now. That is what the second 20% is taken of.

Same percentage. Different amount.
₱20
vs
₱24

Why?

A bigger one: ₱1 200, up 25%, down 25%

UP
25% of ₱1 200 = ₱300
₱1 500
DOWN
25% of ₱1 500 = ₱375
₱1 125

The second amount is always bigger — because the base grew.

Together: ₱800, DOWN 15% first

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.

Does the order matter?
down then up

₱800 → ₱680 → ₱782

up then down

₱800 → ₱920 → ₱782

The same. Remember that — it is tomorrow's lesson.

Your turn — show both amounts

StartChangeThenThe two amountsResult
₱100up 20%down 20%₱20 · ₱24₱96
₱500up 10%down 10%₱50 · ₱55₱495
₱1 200up 25%down 25%₱300 · ₱375₱1 125
₱800down 15%up 15%₱120 · ₱102₱782
₱240up 50%down 50%₱120 · ₱180₱180
Ask every learner this, and only this

“That percentage — of what?

Back to ₱100

crossed out by someone who voted for it

A percentage is always a percentage of something.
Change the something, and you change the amount.

It is not a small effect

₱240
up 50%, down 50%
₱180

A quarter of the value, gone. Bigger percentage, bigger loss.

Tonight's question — do not answer it

You did two calculations for every row today. There is a way to do each row in one.

Exit ticket

A bag costs ₱500. Up 10%. Then down 10%.
  1. Predict — more than ₱500, less, or exactly ₱500?
  2. Work it out in two steps. Write 10% of ______ both times.
  3. One sentence: why is your answer not ₱500?

Quarter sheet. Name at the top. Question 3 is the one that counts.

1 / 15 Up 20%, Down 20% — Percentage Increase and Decrease ← → move · F fullscreen · P print handout