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SUPPLEMENT MULTIPLICATION
[The supplement of a number is the amount by which that number is more than 100]
Find the product of 104 x 106.
(a) Add one of the numbers to the supplement of the other number.
104 + 6 = 110 or 106 + 4 = 110
These are the first two digits of the final product.
(b) Multiply the supplements of the two numbers together. 4 x 6 = 24.
These are the last two digits of the final product.
(c) Combine the two numbers to get your answer.
106 x 104 = 11024
COMPLEMENT MULTIPLICATION
School children find it difficult to compute or perform the multiplication such as 97 x 95.
In mathematics the term COMPLEMENT is used to perform multiplication.
[Complement of a number is the amount by which that number is less than 100.]
Find 97 x 95.
The complement of 97 is 3. The complement of 95 is 5.
(a) Subtract the complement of one of the numbers from the other number.
97 - 5 = 92 or 95 - 3 = 92.
These are the first two digits of your product.
(b) Multiply the complements of the two numbers. 5 x 3 = 15
These are the last two digits of your final product.
(c) Combine the two numbers to get your answer. 97 x 95 = 9215
This method of shortcut works under one condition.
MULTIPLES OF 3
3 times even number
Rule
a. Write half of the multiplier and put 0 at the end.
b. Double the multiplier and subtract it from Rule (a).
Examples:
3 x 2; Half of 2 is 1. Put 0 at the end to form 10.
Take away twice the multiplier. Twice of 2 is 4. 10-4 = 6.
herefore 3 x 2 = 6.
3 x 4; Half of 4 is 2. Put 0 at the end to form 20.
Take away twice the multiplier. Twice of 4 is 8. 20-8 = 12.
Therefore 3 x 4 = 20.
3 x 12; Half of 12 is 6. Put 0 at the end to form 60.
Take away twice the multiplier. Twice of 12 is 24. 60-24 = 36.
Therefore 3 x 12 = 36.
3 time odd number
Rules:
a. Write half of the multiplier (odd number by 2 you get
decimal)
b. Ignore the decimal point and write the number down.
c. Double the multiplier and subtract it from Rule (b).
Examples:
3 x 1; Half of 1 is 0.5. Ignore the decimal decimal point to get 5.
Double of 1 is 2. 5 - 2 = 3. Therefore 3 x 1 = 3.
3 x 7; Half of 3 is 3.5. Ignore the decimal decimal point to form 35.
Double of 7 is 14. 35 - 14 = 21. Therefore 3 x 7 = 21
3 x 19; Half of 19 is 9.5. Ignore the decimal point to form 95.
Double of 19 is 38. 95 - 38 = 57. Therefore 3 x 19 = 57.
MULTIPLES OF 4
4 times even number
Rules:
a. Write half the even number and put 0 at the end.
b. Subtract the same even number from the answer at (a).
Examples:
4 x 2; Half of 2 is 1. Put 0 at the end to form10.
Subtract the 2 from the 10. That is 10 - 2 = 8. Hence 4 x 2 = 8
4 x 4; Half of 4 is 2. Put 0 at the end to form 20.
Subtract the 4 from the 20.That is 20 - 4 = 16. Hence 4 x 4 = 16.
4 x 12; Half of 12 is 6. Put 0 at the end to form 60.
Subtract the 12 from the 60. That is 60 - 12 = 48. Hence 4 x 12 = 48.
4 times odd number
Rules:
a. Write half of the odd multiplier down.
b. Reject the decimal point to get a whole number.
c. Subtract the odd multiplier from the answer at (b).
Examples:
4 x 1; Half of 1 is 0.5. Reject the decimal point to get 5.
Subtract the 1 from the 5. That is 5 - 1 = 4. Hence 4 x 1 = 4.
4 x 3; Half of 3 is 1.5. Reject the decimal point to get 15.
Subtract the 3 from the 25. That is 15 - 3 = 12. Hence 4 x 3 = 12.
4 x 13; Half of 13 1s 6.5. Reject the decimal point to get 65. Subtract
the 13 from the 65. That is 65 - 13 = 52. Hence 4 x 13 = 52. MULTIPLES OF 4
MULTIPLES OF 5
5 times even number
Rules:
Write half of the even multiplier down and put 0 at the end.
Examples:
5 x 2; Half of 2 is 1. Put 0 behind the 1 to form our answer.
Hence 5 x 2 = 10.
5 x 12; Half of 12 is 6. Put 0 behind the 6 to form the correct answer.
Hence 5 x 12 = 60.
5 times odd number
Rules:
Write half of the odd multiplier down and reject the decimal point.
The number you see is your product.
Examples:
5 X 1; Half of 1 is 0.5. Reject the decimal point. Hence 5 x 1 = 5.
5 x 7; Half of 7 is 3.5. Reject the decimal point to get 35.
That is your product.
.
5 x 19; Half of 19 is 9.5. Reject the decimal point to get 95.
This is your product.
MULTIPLES OF 6
6 times even number
Rules:
a. Write half of the even multiplier down.
b. Put the same multiplier behind the number written at (a).
Examples:
6 x 2; Half of 2 is 1. Put the 2 behind the 1 to form your product. Hence 6 x 2 = 12
6 x 8; Half of 8 is 4. Put the 8 behind the 4 to get 48. This is your product.
6 x 14; Half of 14 is 7. Put the 14 behind the 7 to get 714.
Here we have entered into 3-digits. Add the first 2-digits and maintain the last digit.
That is 714 so from here we get 84 as our answer.
Note:
1. When you enter into 3 digits, add the first 2 digits and maintain the last digit.
2. When you enter into four digits, add the 2 middle digits and maintain the last digit.
If the sum of the 2 middle digits exceeds more than a single digit, write the ones
digit down and carry the tens digit to the next column at left.
6 x 22; Half of 22 is 11. Put 22 behind the 11 to get 1122.
Here we have entered into 4 -digits and therefore we add the 2
middle digits 1122 to get 132.
6 x 98; Half of 98 is 49. Put the 98 behind the 49 to get 4998.
Here the sum of the two middle digit is more than 9. Maintain the last digit.
Add the 2 middle digits, maintain the ones digit and carry the tens digit to
the next column at the left.
Hence 4998 which is 4 18 8. This becomes 588. The tens of 18 is carried to 4.
Hence our product is 588.
6 times odd number
Rules:
a. Write half of the odd multiplier down.
b. Reject the decimal point.
c. Add the multiplier to the number at (b) to form your product.
Examples:
6 x 1; Half of 1 is 0.5. Reject the decimal point to get 5.
Add the multiplier to the 5. That is 5 + 1 = 6. This is our product.
6 x 13; Half of 13 is 6.5. Reject the decimal point to get 65.
Add the multiplier to the 65. That is 65 + 13 = 78.
This is our product.
6 x 79; Half of 79 is 39.5. Reject the decimal point to get 395.
Add the multiplier to the 395. That is 395 + 79 = 474. This is our answer.
MULTIPLES OF 7
7 times even number
Rules:
a. Write half of the even multiplier down.
b. Double the multiplier and put it behind the answer at (a).
Examples:
7 x 2; Half of 2 is 1. Double of 2 is 4. Put 4 behind the 1 to get 14.
This is your product.
7 x 6; Half of 6 is 3. Double of 6 is 12. Put the 12 behind 3 to get 312.
We have entered into 3-digits and therefore we add the first 2-digits
and maintain the last digit. That is 312. This gives 42. This is your
answer.
7 x 48; Half of 48 is 24. Double of 48 is 96. Put the 96 behind 24 to get 2496.
Here we have 4-digits and therefore we add the 2-middle digits and
maintain the last digit. 2496 This means 2 13 6.
Since the
sum of the 2-middle digits is more than 9, we maintain the ones- digit
and the tens- digit is carried to the next column. Hence 7 x 48 = 336.
7 times odd number
Rules:
a. Write half of the odd multiplier down.
b. Reject the decimal point.
c. Double the multiplier and add it to the number at (b).
Examples:
7 x 1; Half of 1 is 0.5. Reject the decimal point to get 5. Double of 1 is 2.
Add the 5 and the 2 to get 7. This is your answer.
7 x 9; Half of 9 is 4.5. Reject the decimal point to get 45. Double of 9 is 18.
Add the 45 and the 18 to get 63. This is your answer.
7 x 19; Half of 19 is 9.5. Reject the decimal point to get 95.
Double of 19 is 38. Add the 95 and the 38 to get 133. This is your product.
Since this site is all about making mathematics fun and simple members should bring important discussions such "Prove that 7^0 = 1. A mere greeting will not help.
I hope members are not hurt:(:(:( anyway!
Know that -a^2 means -1 x a^2 and not -a x -a.
The reason is that -a^2 has its coefficient as -1
Therefore -a x -a = a^2 and and not -a^2.
This symbol ^ implies exponent.
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