Tricks and Short-cuts: Part 1

Multiplication using multiples
12 x 15
= 12 x 5 x 3
= 60 x 3
= 180

Multiplication by distribution 
12 x 17
= (12 x 10) + (12 x 7) —> 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 –> 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 —> take the half(0.5) then multiply by 100
18 x 50
= (18/2) x 100 = 18 x 0.5 x 100
= 9 x 100
= 900

Multiplication by 100 —> move the decimal point two places to the right
42 x 100
= 4200 —> added two zeroes

Multiplication by 500 —> take the half(0.5) then multiply by 1000
21 x 500
= 21/2 x 1000
= 10.5 x 1000
= 10500

Multiplication by 25 —> use the analogy $1 = 4 x 25 cents
25 x 14
= (25 x 10) + (25 x 4) —> 250 + 100 —> $2.50 + $1
= 350

Multiplication by 25 —> divide by 4 then multiply by 100
36 x 25
= (36/4) x 100
= 9 x 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 x 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 x 35
first term = [(4 + 1) x 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 x 85
first term = (8 + 1) x 7 = 63
last term = 75
combining first and last terms,
= 6375

15 x 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