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Showing posts with label multiplication. Show all posts
Showing posts with label multiplication. Show all posts

## Friday, January 16, 2009

### Multiplication of 2 numbers that are near to 100 or 1000

This tip is suitable for multiplying two numbers that are near to 100. For example, 103 x 104 and 97 x 98.

Example 1:

To calculate 103 x 104:

1. Add the the ones from the multiplicand to the multiplier.
103 + 4 = 107.

2. Multiply the ones from the multiplier with the ones from the multiplicand.
3 x 4 = 12.

3. Concatenate the results from step 1 and 2. Therefore, 103 x 104 = 10712.

### Example 2:

To calculate 1005 x 1002:

1. Add the the ones from the multiplicand to the multiplier.
1005 + 2 = 1007.

2. Multiply the ones from the multiplier with the ones from the multiplicand. Prepend a zero to the result.
5 x 1 = 010.

3. Concatenate the results from step 1 and 2. Therefore, 1005 x 1002 = 1007010.

### Example 3:

To calculate 97 x 98:

1. Subtract from 10, the ones from multiplicand.
10 - 8 = 2.

2. Subtract from multiplier, the result from step 1.
97 - 2 = 95.

3. Subtract from 10, the ones from multiplier.
10 - 7 = 3.

4. Multiply the result from step 3 with the result from 1. Prepend a zero.
2 x 3 = 06.

5. Concatenate the results from step 2 and step 4. Therefore, 97 x 98 = 9506.

### Example 4:

To calculate 993 x 995:

1. Subtract from 10, the ones from multiplicand.
10 - 5 = 5.

2. Subtract from multiplier, the result from step 1.
993 - 5 = 988.

3. Subtract from 10, the ones from multiplier.
10 - 3 = 7.

4. Multiply the result from step 3 with the result from 1. If you get a one digit number, prepend two zeroes, otherwise prepend just one zero.
5 x 7 = 035.

5. Concatenate the results from step 2 and step 4. Therefore, 993 x 995 = 988035.

### Exercise:

If domain name is cost \$9.90 each, what is the cost if you want to buy 92 domain?

## Thursday, January 15, 2009

### Multiplication of any number by a number near 100

It is easy to multiply any number by 100. We just need to append two zeroes to the end of that multiplicand number. For example, 100 x 23 = 2300. But, what if the multiplier is a number that is near to 100, such as 101, or 99?

To multiply a number, a, by a number, b, that is near to 100, here are the steps.

1. Multiply the multiplicand by 100.
c = 100 x b

2. Subtract 100 from the multiplier.
d = b - 100

3. Multiply multiplicand, a with the result from step 3, d.
e = d x a

4. Finally, add the result from steps 1 and 3.

In simple words, we could write it as
( 100 x multiplicand ) + ( (multiplier - 100) x multiplicand )

### Example:

1. 101 x 23 = (100 x 23) + ( (101 - 100) x 23 ) = 2300 + (1 x 23) = 2300 + 23 = 2323

2. 99 x 23 = (100 x 23) + ( (99 - 100) x 23 ) = 2300 + (-1 x 23) = 2300 - 23 = 2277

Now, you can try to do it on larger numbers such as 101 x 297, or even slightly larger or smaller than 100 multiplier, such as 103 x 74.

## Friday, September 12, 2008

### Multiply a number by 11

Multiplying a one digit number by 11, is easy. For example, 2 x 11 = 22. We just repeat the number back twice.

What if we have 1334 x 11? This strategy could help us to multiply any greater than 2 digits number by 11.

The best way to explain this strategy is by using examples.

Example 1: 243 x 11.

1. 2 _ _ 3   (3 digits - put extra 2 blanks in the middle)

2. 2 2+4 _ 3   (add the 1st 2 numbers)

3. 2 6 4+3 3   (add the last 2 numbers)

4. 2 6 7 3

Therefore, 243 x 11 = 2673

Example 2: 1435 x 11.

1. 1 _ _ _ 5  (4 digits - put extra 3 blanks in the middle)

2. 1 1+4 4+3 3+5 5 = 15785

Therefore, 1435 x 11 = 15785

Note:

If the addition of the 2 numbers would gives 2 digits number, add that number's left digit to the left digit of the original number.

Example 3: 99x 11.

Wrong: 99 x 11 = 9 9+9 9 = 9189

Note that 9 + 9 = 18 (a 2 digits number).

1. 9 _ 9

2. 9 9+9 9

3. 9 18 9 ---> 9 + 1 8 9

4. 1089

Example 4: 46 x 11.

46 x 11 = 4 4+6 6 = 4 10 6 = 4 +1 0 6 = 506

As a conclusion, to multiply a number by 11, add the digits of a 2 digits number, and place the sum between them. If the addition produce a more than 1 digit number, carry the tens column to the left.

## Monday, August 11, 2008

### Product of a single digit number with 9

This algorithm is useful for kids that are lazy enough to memorize the multiplication table of 9.

The algorithm works like this:

Suppose you want a product of n and 9, you can do

1. n - 1

2. 10 -n

3. The answer is (n-1) as the first digit and (10 - n) as the second digit.

Example:

4 x 9 =36

First digit: 4 - 1 = 3

Second digit: 10 - 4 = 6

Note: This trick only works on multiplication of any single digit number with 9.

## Thursday, April 24, 2008

### Box multiplication

The box multiplication technique is suitable for people that has problem with numbers, since it will organized all the number in place.

Example 1:

13 × 23 = 299 First, draw a box for each number. Divide each box diagonally, with a straight line. Then multiply diagonally to the right. For example, 3 × 2 = 6. Put 0 inside the left triangle and 6 inside the right triangle, and so on.

After we have fill in all the numbers inside the triangle, add all the numbers diagonally to the left. For example 6 + 0 + 3 = 9, 0 + 2 + 0 = 2. Write the addition at the end. Follow the arrow.

Example 2:

79 × 85 = 6715 In this example, when we add 2, 4 and 5, we get 11. So, we write 1 and carry 1 (just write it in bracket). Next, when we want to add 7, 6 and 3, add the carry number as well. So, it will become 7 + 6 + 3 + 1 = 17. The same thing goes here. Write 7 and carry 1. The last one is 5 + 1 = 6.

note: The box multiplication technique could also be applied to the numbers that are more than two digits, such as 234 × 346 and 342 × 34.

## Tuesday, April 22, 2008

### Multiply two 3 digits numbers in your head

This article will show how to do multiplication of two three digits numbers from right to left. Consider 234 × 456.

Step 1: Multiply the last digits. Write 2, carry 4.

Step 2: Cross multiply the one and the tenth, and add them together. We get 53. Add the 4 that we carry to 53. We get 57. Write 7, carry 5.

Step 3: Multiply all digits, like in the figure below. We get 55. Add the 5 that we carry to 55. We get 60. Write 0, carry 6.

Step 4: Finally, multiply the two left digits. We get 22. Add the 6 that we carry to 22. Write 2, carry 2.

Step 5: Finally, multiply the left digits. Add the 2 that we carry to 8. We get 10. Write both numbers.

Therefore, the answer is 108072.

## Thursday, April 17, 2008

### Easy Multiplication I

This technique of multiplication will do the multiplication from right to left. Let’s look at an example. 23 x 12 = 276

Step 1: Multiply the last digits.

Step 2: Cross multiply both sets of numbers and add them together.

Step 3: Finally, multiply the left digits.