Multiplication by triplex numbers
As we have seen, multiplication by a triplex number is interesting and easy. Last week we saw how to multiply a three-digit number by a triplex number. Now using the same method we are going to multiply a number with more digits by a triplex umber.
To multiply any number by a triplex number we include zeros before and after the given number so that we don’t miss any digit. Let us see an example with a five-digit number
Example: 15632 x 222
001563200 x 222
●Starting from the right add every three digits and multiply by 2.
●(0 + 0 + 2) x 2 = 4 – the units digit of the answer
●(0 + 2 +3) x 2 = 10 – 0 the next digit, 1 carried over
●(2 + 3 + 6) x 2 = 22 – 3(2+1) the next digit, 2 carried over
●(3 + 6 + 5) x 2 = 28 – 0(8+2) the next digit, 3(2+1) carried over
●(6 + 5 + 1) x 2 = 24 – 7(4+3) the next digit, 2 carried over
●(5 + 1 + 0) x 2 = 12 – 4(2+2) the next digit, 1 carried over
●(1 + 0 + 0) x 2 = 2 – 3(2+1) the next digit
Answer: 3470304
Using this method of including zeros we can also multiply a two-digit number by a triplex number.
Example: 45 x 666
004500 x 666
●(0 + 0 + 5) x 6 = 30 – put down 0, carry 3
●(0 + 5 + 4) x 6 = 54 – put down 7, carry 5
●(5 + 4 + 0) x 6 = 54 – put down 9, carry 5
●(4 + 0 + 0) x 6 = 24 – put down 29
Answer: 29970
Let us try a problem with more digits.
2131522 x 555
00213152200 x 555
Group digits in threes, add up each group and multiply by 5.
(0+0+2)(0+2+2)(2+2+5)(2+5+1)(5+1+3)(1+3+1)(3+1+2)(1+2+0)(2+0+0)
2 4 9 8 9 5 6 3 2
X 5
10 2045404525 301510
Answer: 1182994710
Some problems to try: 2468 x 444, 19112 x 333, 46123 x 888