Banking Maths Tricks and Short-cuts

Banking Maths Tricks and Short-cuts

MULTIPLICATION:


Multiplication using multiples

12 × 15
= 12 × 5 × 3
= 60 × 3
= 180

Multiplication by distribution 

12 × 17
= (12 x 10) + (12 x 7) `rArr` 12 is multiplied to both 10 & 7
= 120 + 84
= 204

Multiplication by “giving and taking”

12 x 47
= 12 x (50 – 3)
= (12 x 50) – (12 x 3)
= 600 – 36
= 564

Multiplication by 5 `rArr` take the half(0.5) then multiply by 10

428 x 5
= (428 x 1 `-:` 2) x 10 = 428 x 0.5 x 10
= 214 x 10
= 2140

Multiplication by 10 ⇒ just move the decimal point one place to the right

14 x 10
= 140 added one zero

Multiplication by 50 `rArr` take the half(0.5) then multiply by 100

18 x 50
= (18÷2) × 100 = 18 × 0.5 × 100
= 9 x 100
= 900

Multiplication by 100 move the decimal point two places to the right

42 × 100
= 4200 added two zeroes

Multiplication by 500 take the half(0.5) then multiply by 1000

21 × 500
= 21 ÷ 2 × 1000
= 10.5 × 1000
= 10500

Multiplication by 25 use the analogy $1 = 4 x 25 cents

25 × 14
= (25 × 10) + (25 × 4) → 250 + 100 →  $2.50 + $1
= 350

Multiplication by 25 divide by 4 then multiply by 100

36 × 25
= (36 ÷ 4) × 100
= 9 × 100
= 900Multiplication by 11 if sum of digits is less than 10
72 x 11
= 7_2 the middle term = 7 + 2 = 9
= place the middle term 9 between 7 & 2
= 792Multiplication by 11 if sum of digits is greater than 10
87 x 11
= 8_7 the middle term = 8 + 7 = 15
because the middle term is greater than 10, use 5 then
add 1 to the first term 8, which leads to the answer of
= 957

Multiplication of 37 by the 3, 6, 9 until 27 series of numbers the “triple effect” 
solve 37 x 3
multiply 7 by 3 = 21, knowing the last digit (1), just combine two more 1’s giving the triple digit answer 111solve 37 x 9
multiply 7 by 9 = 63, knowing the last digit (3), just combine two more 3’s giving the triple digit answer 333

solve 37 x 21
multiply 7 by 21 = 147, knowing the last digit (7), just combine two more 7’s giving the triple digit answer 777

Multiplication of the “dozen teens” group of numbers —
(i.e. 12, 13, 14, 15, 16, 17, 18, 19) by ANY of the numbers within the group:

solve 14 x 17
4 × 7 = 28;  remember 8, carry 2
14 + 7 = 21
add 21 to whats is carried (2)
giving the result 23
form the answer by combinig 23 to what is remembered (8)
giving the answer 238

 

 

Multiplication of numbers ending in 5 with difference of 10
45 × 35
first term = [(4 + 1) × 3] = 15; (4 is the first digit of 45 and 3 is the first digit of 35 → add 1 to the higher first digit which is 4 in this case, then multiply the result by 3, giving 15)
last term = 75
combining the first term and last term,
= 157575 × 85
first term = (8 + 1) x 7 = 63
last term = 75
combining first and last terms,
= 6375

15 × 25
= 375

Multiplication of numbers ending in 5 with the same first terms (square of a number)

25 x 25
first term = (2 + 1) x 2 = 6
last term = 25
answer = 625 ⇒ square of 25

75 x 75
first term = (7 + 1) x 7 = 56
last term = 25
answer = 5625 ⇒ 75 squared

DIVISION:


Division by parts ⇒ imagine dividing $874 between two persons

874 ÷ 2
= 800 ÷ 2 + 74 ÷ 2
= 400 + 37
= 437

Division using the factors of the divisor: “double division”

70 ÷ 14
= (70 ÷ 7) ÷ 2 ⇒ 7 and 2 are the factors of 14
= 10 ÷ 2
= 5

Division by using fractions:

132 ÷ 2
= (100 ÷ 2 + 32 ÷ 2) ⇒ break down into two fractions
= (50 + 16)
= 66

Division by 5 ⇒ divide by 100 then multiply by 20

1400 ÷ 5
= (1400 ÷ 100) x 20
= 14 x 20
= 280 Division by 10 ⇒ move the decimal point one place to the left
0.5 ÷ 10
= 0.05 ⇒ 5% is 50% divided by ten

Division by 50 divide by 100 then multiply by 2

2100 ÷ 50
= (2100 ÷ 100) x 2
= 21 x 2
= 42700 ÷ 50
= (700 ÷ 100) x 2
= 7 x 2
= 14

Division by 100 —> move the decimal point two places to the left
25 ÷ 100
= 0.25

Division by 500 —> divide by 100 then multiply by 0.2

17 ÷ 500
= (17 ÷ 100) x 0.2
= 0.17 x 0.2
= 0.034

Division by 25 —> divide by 100 then multiply by 4 

500 ÷ 25
= (500 ÷ 100) x 4
= 5 x 4
= 20

750 ÷ 25
= (750 ÷ 100) x 4
= 7.5 x 2 x 2
= 30

ADDITION:


Addition of numbers close to multiples of ten (e.g. 19, 29, 89, 99 etc.)

116 + 39
= 116 + (40 – 1)
= 116 + 40 – 1 —> add 40 then subtract 1
= 156 – 1
= 155116 + 97
= 116 + (100 – 3)
= 116 + 100 – 3 —> add 100 then subtract 3
= 216 – 3
= 213

Addition of decimals

12.5 + 6.25
= (12 + 0.5) + (6 + 0.25)
= 12 + 6 + 0.5 + 0.25 —> add the integers then the decimals
= 18 + 0.5 + 0.25
= 18.75

SUBTRACTION:


Subtraction by numbers close to 100, 200, 300, 400, etc.

250 – 96
= 250 – (100 – 4)
= 250 – 100 + 4 —> subtract 100 then add 4
= 150 + 4
= 154250 – 196
= 250 – (200 – 4)
= 250 – 200 + 4 —> subtract 200 then add 4
= 50 + 4
= 54

216 – 61
= 216 – (100 – 39)
= 216 – 100 + 39
= 116 + (40 – 1) —> now the operation is addition, which is much easier
= 156 – 1
= 155

Subtraction of decimals

47 – 9.9
= 47 – (9 + 0.9) —> “double subtraction”
= 47 – 9 – 0.9 —> subtract the integer first then the decimal
= 38 – 0.9
= 37.1

18.3 – 0.8
= 18 + 0.3 – 0.8
= (18 – 0.8) + 0.3 —> subtract 0.8 from 18 first
= 17.2 + 0.3
= 17.5

WORKING ON PERCENTAGES:

30% of 120
= 10% x 3 x 120 —> it is much easier working with tens (10%)
= 10% x 120 x 3
= 12 x 3
= 36

five percent of a number: 5%

360 x 5%
= 360 x 10% ÷ 2 —> take the 10% and divide by 2
= 36 ÷ 2
= 18360 x 5%
= 360 x 50% ÷ 10 —> take the half(0.5) and divide by 10
= (360 ÷ 2) ÷ 10
= 180 ÷ 10
= 18

ninety percent of a number: 90%

90% of 700
= (100% – 10%) x 700
= (100% x 700) – (10% x 700) —> 100% minus 10% of the number
= 700 – 70
= 630

What is 18 as a percentage of 50?

= 18 ÷ 50
= (18 ÷ 100) x 2 ⇒ method: division by 50 (explained above)
= 0.18 x 2
= 0.36
= 36%

What is 132 as a percentage of 200?

= 132 ÷ 200
= (132 ÷ 2) ÷ 100
= [100 ÷ 2 + 32 ÷ 2] ÷ 100 —> solution by “double division”
= (50 + 16) ÷ 100
= 66 ÷ 100
= 0.66
= 66%

What is 270 as a percentage of 300?

= 270 ÷ 300
= [(270/3) ÷ 100] —> “double division” (using the factors of 300)
= 90 ÷ 100
= 90%

What is 17 as percentage of 500?

= 17 ÷ 500
= (17 ÷ 50) ÷ 10
= (17 ÷ 100) x 2 ÷ 10 —> solution using the procedure: division by 50
= (0.17 x 2) ÷ 10
= 0.34 ÷ 10
= 0.034
= 3.4 %

percentages close to 100:

95% of 700
= (100% – 5%) x 700
= (100% x 700) – (5% x 700)
= 700 – (10% x 700 ÷ 2) → 5% is 10% ÷ 2
= 700 – 70 ÷ 2
= 700 – 35
= 665

percentages less than 10 percent:

3% of 70
= (3 ÷ 100) x 70
= (70 ÷ 100) x 3 ⇒ divide by 100 then multiply the percent value
= 0.7 x 3
= 2.1

DECIMALS:

To convert or express percentages as decimals, divide by 100 or simply just move the decimal point by two places to the left of the given number, thus:1% = 1/100 = 0.01
2% = 2/100 = 0.02 = 1/50
3% = 3/100 = 0.03
4% = 4/100 = 0.04 = 1/25
5% = 5/100 = 0.05 = 1/20
6.25% = 6.25/100 = 0.0625 = 1/16
7% = 7/100 = 0.07
7.5% = 7.5/100 = 0.075
10% = 10/100 = 0.1 = 1/10
12.5% = 12.5/100 = 0.125 = 1/8
20% = 0.2 = 1/5
21% = 0.21
25% = 0.25 = 1/4
30% = 0.3 = 3/10
33.33% = 33.33/100 = 0.3333 = 1/3
37.5% = 0.375 = 3/8
40% = 0.4 = 2/5
50% = 0.5 = 1/2
60% = 0.6 = 3/5
62.5% = 0.625 = 5/8
66.66% = 66.66/100 = 2/3
75% = 0.75 = 3/4
80% = 0.8 = 4/5
87.5% = 0.875 = 7/8
100% = 1
125% = 1.25 = 1 1/4
150% = 1.5 = 1 1/2
200% = 2

FRACTIONS:


What is three quarters of 80?

= 3/4 x 80
= (80/4) x 3 —> divide by 4 then multiply by 3
= 20 x 3
= 60How many quarters in two and a half?
2.5/.25
= 10 —> there are 10 quarters in $2.50
Improper fractions:

3/2 = 1 1/2 = 1.5 = 150%

4/3 = 1 1/3 = 1.3333 = 133.33% —> useful number for volume of sphere, etc.

9/5 = 1 4/5 = 1.8 = 180% —> conversion factor for Celsius/Fahrenheit temperatures


V = 4/3 pi * r^3

where:
V = volume of sphere
r = radius of sphere


F = (1.8 C) + 32

where:
F = temperature in Fahrenheit
C = temperature in Celsius

Square Number

Tips 1: 2 Digit Number which ends in 5
Step1: Multiply the first digit of number, with the next to its number. Ex: 35 is the number you want to square. 3 x 4 = 12
Step2: Finally add 25 at the end of the result.

Answer: 1225

Tips 2: Any 2 Digit Number
Ex: 47
Step1: Look for the nearest 10 boundary.
3 from 47 to 50
Step2: Since we went up 3 to 50, now go down 3 from 47 to 44.
Step3: Now mentally multiply 44 x 50 = 2200 – 1st answer.
Step4: 47 is 3 away from the 10 boundary 50, Square 3 as 9 – 2nd answer.
Step5: Add the first and second answer, 2200 + 9

Answer: 2209

Sequential Inputs of numbers with 8

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

Sequential 1’s with 9

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

Sequential 8’s with 9

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

Numeric Palindrome with 1’s

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Without 8

12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 27 = 333333333

12345679 x 36 = 444444444

12345679 x 45 = 555555555

12345679 x 54 = 666666666

12345679 x 63 = 777777777

12345679 x 72 = 888888888

12345679 x 81 = 999999999

Sequential Inputs of 9

9 x 9 = 81

99 x 99 = 9801

999 x 999 = 998001

9999 x 9999 = 99980001

99999 x 99999 = 9999800001

999999 x 999999 = 999998000001

9999999 x 9999999 = 99999980000001

99999999 x 99999999 = 9999999800000001

999999999 x 999999999 = 999999998000000001

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