## Thursday, March 12, 2009

### How to solve simultaneous equations by Elimination

Example 1:

Example 2:

## Tuesday, January 13, 2009

### Shortcuts for Divisibility by 10,11, 12 and 15

**Divisibility by 10:**

How to check a number is divisible by 10?

It is very simple, check for the units digit of the number, if it is 0, then the number is clearly divisible by 10.

**Examples:**

Is the number 1234567890 divisible by 10?

Check for the unit digit, it is 0,

5 + 7 + 2 + 2 + 5 + 8 + 3 + 4 = 36

So 1234567890 is divisible by 10.

Is the number 1236985 divisible by 10?

The unit digit is not zero, so the number 1236985 is not divisible by 10.

**Divisibility by 11:**

How to check a number is divisible by 11?

It is very simple, check the number, if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.

**Examples:**

Is the number 2547039 divisible by 11?

First find the difference between sum of its digits at odd and even places.

(Sum of digits at odd places) - (Sum of digits at even places)

= (9 + 0 + 4 + 2) - (3 + 7 + 5)

= 15 - 15 = 0

The number is 0, so the number 2547039 is divisible by 11.

Is the number 13165648 divisible by 11?

(Sum of digits at odd places) - (Sum of digits at even places)

= (8 + 6 + 6 + 3) - (4 + 5 + 1 + 1)

= 23 - 11 = 12

The number is 12, so the number 13165648 is not divisible by 11.

**Divisibility by 12:**

How to check a number is divisible by 12?

It is very simple, check the number is divisible by 3 and 4, if it is divisible by both, then clearly the number is divisible by 12.

**Examples:**

Is the number 59175432 divisible by 12?

First check the number is divisible by 3,

5 + 9 + 1 + 7 + 5 + 4 + 3 + 2 = 36

36 is divisible by 3, so the number is also divisible by 3.

Then check the number is divisible by 4 also,

The last two digit of the number is 32.

32 is divisible by 4, so the number is also divisible by 4.

The number 59175432 is divisible both by 3 and 4, so it is divisible by 12.

Is the number 39737094 divisible by 12?

3 + 9 + 7 + 3 + 7 + 0 + 9 + 4 = 42.

42 is divisible by 3, so the number is also divisible by 3.

Now check the number is divisible by 4 also,

The last two digit of the number is 94.

94 is not divisible by 4, so the number is not divisible by 4

The number 39737094 is divisible only by 3 and not by 4, so it is not divisible by 12

**Divisibility by 15:**

How to check a number is divisible by 15?

It is very simple, check the number is divisible by 3 and 5, if it is divisible by both, then clearly the number is divisible by 15.

**Examples:**

Is the number 469192440 divisible by 15?

First check the number is divisible by 3,

4 + 6 + 9 + 1 + 9 + 2 + 4 + 4 + 0 = 39

39 is divisible by 3, so the number is also divisible by 3.

Then check the number is divisible by 5 also,

Check the units digit in the given number

unit digit is 0, so the number is also divisible by 5.

The number 469192440 is divisible both by 3 and 5, so it is divisible by 15.

Is the number 326643 divisible by 15?

3 + 2 + 6 + 6 + 4 + 3 = 24.

24 is divisible by 3, so the number is also divisible by 3.

Now check the number is divisible by 5 also,

The units digit is not 0 or 5, so the number is not divisible by 5

The number 326643 is divisible only by 3 and not by 5, so it is not divisible by 15.Source: http://www.helpwithassignemnt.com

## Sunday, January 11, 2009

### Shortcuts for Divisibility by 5, 6 , 8 and 9

Divisibility by 5:

How to check a number is divisible by 5?

It is very simple, check for units digit, if it is either 5 or 0, then clearly the number is divisible by 5.

Examples:

Is the number 13356890 divisible by 5?

Check the units digit in the given number

unit digit is 0, so 13356890 is divisible by 5.

Is the number 56722368553 divisible by 5?

The units digit is not 0 or 5, so the number 56722368553 is not divisible by 5.

Divisibility by 6:

How to check a number is divisible by 6?

It is very simple, check the number is divisible by 2 and 3, if it is divisible by both, then clearly the number is divisible by 6.

Examples:

Is the number 3246546 divisible by 6?

First check the number is divisible 2,

its unit digit is 6, which is divisible by 2.

Then check the number is divisible 3 also,

3 + 2 + 4 + 6 + 5 + 4 + 6 = 30

30 is divisible by 3, so the number is also divisible by 3

The number 3246546 is divisible both by 2 and 3, so it is divisible by 6.

Is the number 128956 divisible by 6?

Its unit digit is 6, which is divisible by 2.

Now check the number is divisible 3 also,

1 + 2 + 8 + 9 + 5 + 6 = 31

31 is not divisible by 3, so the number is not divisible by 3

The number 128956 is divisible only by 2 and not by 3, so it is not divisible by 6

Divisibility by 8:

How to check a number is divisible by 8?

It is very simple, check whether the last three digits of the number is divisible by 8, if it is, then the number is divisible by 8.

Examples:

Is the number 7377473496 divisible by 8?

Take the last three digits of the number.

Last three digit is 496, check whether it is divisible by 8.

496 is divisible by 8, So the number 7377473496 is divisible by 8.

Is the number 546632318 divisible by 8?

The last three digit is 318.

318 is not divisible by 8, so the number 546632318 is not divisible by 8.

Divisibility by 9:

How to check a number is divisible by 9?

It is very simple, first sum all the digits of the number, now check whether the result is divisible by 9. If the answer is divisible by 9, clearly the number will be divisible by 9. It is similar to divisibility of 3.

Examples:

Is the number 57225834 divisible by 9?

Now, sum the digits of the number,

5 + 7 + 2 + 2 + 5 + 8 + 3 + 4 = 36

36 is divisible by 9, so 57225834 is divisible by 9.

Is the number 3216763132 divisible by 3?

3 + 2 + 1 + 6 + 7 + 6 + 3 + 1 + 3 + 2 = 34

34 is not divisible by 9, so the number 3216763132 is not divisible by 9.

### Shortcuts for Divisibility by 2,3 and 4

Divisibility by 2:

How to check a number is divisible by 2?

It is very simple, first we should check the units digit of the number, whether it is divisible by 2. A number is divisible by 2, only when its unit digit contains 0, 2, 4, 6, 8.

Examples:

Is the number 6542646882 divisible by 2?

Now, check the units digit of the number, it is 2, so 6542646882 is divisible by 2.

Divisibility by 3:

How to check a number is divisible by 3?

It is very simple, first sum all the digits of the number, now check whether the result is divisible by 3. If the answer is divisible by 3, clearly the number will be divisible by 3.

Examples:

Is the number 6466545 divisible by 3?

Now, sum the digits of the number,

6 + 4 + 6 + 6 + 5 + 4 + 5 = 36

36 is divisible by 3, so 6466545 is divisible by 3.

Is the number 544733369 divisible by 3?

5 + 4 + 4 + 7 + 3 + 3 + 3 + 6 + 9 = 44

44 is not divisible by 3, so the number 544733369 is not divisible by 3.

Divisibility by 4:

How to check a number is divisible by 4?

It is very simple, first check the last two digits of the number is divisible by 4, then the number will be divisible by 4.

Examples:

Is the number 98731812 divisible by 4?

Take the last two digits in the given number,

Last two digit is 12, which is divisible by 4,

So 98731812 is divisible by 4.

Is the number 3426941365 divisible by 4?

The last two digit of the number is 65, which is not divisible by 4,

So the number 3426941365 is not divisible by 4.

## Friday, December 19, 2008

### Multiplying by 25 and 125

To multiply by 25 you multiply by 100 (just add two 0’s to the end of the number) then divide by 4, since 100 = 25×4. Note: to divide by 4 your can just divide by 2 twice, since 2×2 = 4.

64×25 = 6400/4 = 3200/2 = 1600.

58×25 = 5800/4 = 2900/2 = 1450.

To multiply by 125, you multiply by 1000 then divide by 8 since 8×125 = 1000. Notice that 8 = 2×2x2. So, to divide by 1000 add three 0’s to the number and divide by 2 three times.

32×125 = 32000/8 = 16000/4 = 8000/2 = 4000.

48×125 = 48000/8 = 24000/4 = 12000/2 = 6000.

### Multiplying by 9, or 99, or 999

· Multiplying by 9 is really multiplying by 10-1.

· So, 9×9 is just 9x (10-1) which is 9×10-9 which is 90-9 or 81.

· Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414.

· One more example: 68×9 = 680-68 = 612.

· To multiply by 99, you multiply by 100-1.

· So, 46×99 = 46x (100-1) = 4600-46 = 4554.

· Multiplying by 999 is similar to multiplying by 9 and by 99.

· 38×999 = 38x(1000-1) = 38000-38 = 37962

### The 11 Rule

To multiply any two digit number by 11:

For this example we will use 34.

· Separate the two digits in you mind (3__4).

· Notice the hole between them!

· Add the 6 and the 4 together (3+4=7)

· Put the resulting 7 in the hole 374. That's it! 11 x 34=374

Source: http://www.helpwithassignment.com