Percent · Teknikguide
Percentages in Your Head
Av Robert Hansson, Kung Fu Math
Percent means per hundred. Discounts, tips, taxes, interest and test scores are all percentages, so this is one of the most useful mental skills you can build.
You do not need a calculator for most of them. Two building blocks, 10 % and 1 %, plus a handful of fraction equivalents, cover almost every everyday percentage.
01
10 % and 1 % building blocks
10 % of a number is the number divided by 10. 1 % is the number divided by 100. Build any percentage from these: 15 % is 10 % plus half of it; 35 % is three tens plus a five.
Löst exempel
15 % of 240
- → 10 % of 240 = 24
- → 5 % is half of that: 12
- → 24 + 12 = 36
Svar: 36
Öva: Try 20 % of 85, 35 % of 60 and 12 % of 300.
02
Flip the percentage
x % of y is always the same as y % of x. 8 % of 25 sounds awkward, but 25 % of 8 is simply a quarter of 8.
Löst exempel
8 % of 25
- → Flip it: 25 % of 8
- → A quarter of 8 = 2
Svar: 2
Öva: Try 4 % of 75, 18 % of 50 and 36 % of 25.
03
Fraction equivalents
Learn the common pairs: 50 % = 1/2, 25 % = 1/4, 20 % = 1/5, 12.5 % = 1/8, 75 % = 3/4. Then a percentage becomes a simple division.
Löst exempel
12.5 % of 64
- → 12.5 % is 1/8
- → 64 ÷ 8 = 8
Svar: 8
Öva: Try 75 % of 48, 20 % of 135 and 12.5 % of 400.
04
Increase and decrease
To increase by a percentage, multiply by 1 plus the rate. A 20 % rise means × 1.2. A 20 % discount means paying 80 %, which is × 0.8. One multiplication instead of two steps.
Löst exempel
A 30 % discount on 70
- → You pay 70 %
- → 10 % of 70 is 7
- → 7 × 7 = 49
Svar: 49
Öva: Increase 50 by 12 %, reduce 160 by 25 % and increase 80 by 5 %.
05
Fraction to percent
To turn a fraction into a percentage, scale it to hundredths or divide. 3/4 is 75/100. For thirds, remember 1/3 ≈ 33.3 % and 2/3 ≈ 66.7 %; the last digit rounds up because 66.666… is closer to 66.7.
Löst exempel
2/3 as a percentage
- → 1/3 = 33.333… %
- → Double it: 66.666… %
- → Rounded to one decimal: 66.7 %
Svar: 66.7 %
Öva: Try 3/8, 5/6 and 7/20 as percentages.
Vanliga misstag
- Adding percentages of different totals. A 10 % rise followed by a 10 % fall does not bring you back to the start.
- Confusing percentage points with percent. Going from 20 % to 25 % is 5 percentage points, but a 25 % increase.
- Truncating instead of rounding. 2/3 is 66.7 %, not 66.6 %.
Sammanfattning
- Build percentages from 10 % and 1 %.
- Flip awkward percentages and use fraction equivalents.
- Use a single multiplier for increases and discounts.
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