31 cardsUCAT
UCAT Mental Maths and Percentage Shortcuts
31 flashcards on percentage shortcuts, fractions, ratios and quick multiplication for the UCAT Quantitative Reasoning subtest. Original study material for practice.
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10 per cent of a number
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1
10 per cent of a number
Move the decimal point one place left. 10% of 340 = 34.
2
5 per cent of a number
Find 10% and halve it. 5% of 340 = 17.
3
1 per cent of a number
Divide by 100. 1% of 340 = 3.4.
4
15 per cent of a number
Add 10% and 5%. 15% of 80 = 8 + 4 = 12.
5
20 per cent of a number
Find 10% and double it, or divide by 5. 20% of 65 = 13.
6
25 per cent of a number
Divide by 4. 25% of 84 = 21.
7
75 per cent of a number
Find 25% and multiply by 3, or subtract 25% from the whole. 75% of 84 = 63.
8
12.5 per cent of a number
Divide by 8. 12.5% of 64 = 8.
9
33 and one third per cent
Divide by 3. 33 1/3% of 90 = 30.
10
Adding VAT at 20 per cent
Multiply by 1.2. A price of 50 pounds becomes 60 pounds.
11
Removing VAT at 20 per cent from a price that includes it
Divide by 1.2. 60 pounds including VAT was 50 pounds before VAT.
12
Percentage increase formula
(New - Old) / Old x 100. From 40 to 50: 10/40 x 100 = 25%.
13
Percentage decrease formula
(Old - New) / Old x 100. From 50 to 40: 10/50 x 100 = 20%.
14
Why a 25 per cent rise then a 25 per cent fall does not return to the start
The fall applies to a larger number. 100 x 1.25 x 0.75 = 93.75.
15
Reverse percentage
If a price after a 20% discount is 64, divide by 0.8 to get the original, 80.
16
Percentage points versus per cent
A rise from 30% to 36% is 6 percentage points but a 20% relative increase (6/30).
17
Fraction to percentage: 1/8
12.5%
18
Fraction to percentage: 3/8
37.5%
19
Fraction to percentage: 1/5
20%
20
Fraction to percentage: 2/3
66.7% (66 2/3%)
21
Multiply by 5 quickly
Multiply by 10 and halve. 36 x 5 = 360 / 2 = 180.
22
Multiply by 25 quickly
Multiply by 100 and divide by 4. 32 x 25 = 3200 / 4 = 800.
23
Multiply by 11 (two-digit numbers)
Put the digit sum between the digits. 43 x 11 = 4(4+3)3 = 473.
24
Multiply by 9
Multiply by 10 and subtract the number. 7 x 9 = 70 - 7 = 63; 47 x 9 = 470 - 47 = 423.
25
Squaring a number ending in 5
Multiply the tens digit by the next integer, then append 25. 35^2 = (3 x 4) then 25 = 1225.
26
Speed, distance, time triangle
Distance = speed x time; speed = distance / time; time = distance / speed.
27
Converting minutes to a decimal of an hour
Divide by 60. 45 min = 0.75 h; 20 min = 0.333 h.
28
Ratio sharing
Add the parts, find one part, then multiply. Share 60 in 2:3 gives 5 parts, 12 each, so 24 and 36.
29
Currency conversion direction
If the rate is quoted as 1 GBP = 1.2 euros, multiply by 1.2 to go from pounds to euros and divide by 1.2 to go back. 60 GBP = 72 euros; 60 euros = 50 GBP.
30
Estimating with rounding
Round figures to one or two significant figures, calculate, then choose the closest option. 4.9 x 61 is about 5 x 60 = 300.
31
Mean from a total
Mean = total / number of values. If the mean of 5 numbers is 12, the total is 60.
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