Percent of What?

Percentage increase and decrease — and why up 20% then down 20% does not bring you back.

MATHEMATICS 7 MATATAG · Key Stage 3
CG Quarter 1 · competency 7
Term 1 · Week 7

The two-column ledger — ₱100, up 20%, then down 20%

Up 20%
20% of ₱100 = ₱20
₱100 + ₱20 =
₱120
Down 20%
20% of ₱120 = ₱24
₱120 − ₱24 =
₱96
₱20
same 20% · different base
₱24
A percentage is always a percentage of something.
Change the something, and you change the amount.

Build any percentage from these two

10%
move the digits one place
1%
move them two places
5%
half of 10%
20%
double 10%
15%
10% + 5%
25%
a quarter — halve, halve
12%
10% + 1% + 1%
35%
10%×3 + 5%

Worked: 12% of ₱250 → 10% is ₱25, 1% is ₱2.50, so 12% is 25 + 2.50 + 2.50 = ₱30. No formula, no calculator.

The multiplier — one step instead of two

ChangeIncrease ×Decrease ×
5%1.050.95
10%1.100.90
12%1.120.88
15%1.150.85
20%1.200.80
25%1.250.75
35%1.350.65
50%1.500.50

+p% is × (1 + p/100). −p% is × (1 − p/100). And Day 1 in one line: 1.20 × 0.80 = 0.96.

Discounts do not add

50% off then 20% off = 70% off
= 60% off

0.50 × 0.80 = 0.40, so you pay 40% and save 60%. The second 20% is taken of the sale price, not the original.
₱1 000 → ₱500 → ₱400.

Percent of what? Change the what, and you change the amount.
MATATAG Mathematics CG (DepEd, August 2023), p. 52
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