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.

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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

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627

Source: http://www.helpwithassignment.com

Maths shortcut

Here’s a collection of time-saving math shortcuts, great for back-of-the-envelope estimates

Shortcut to multiplication

Square Number

Tips 1: 2 Digit Number which ends in 5
Step1: Multiply the first digit of number, with the next to its number. Ex: 45 is the number you want to square. 4 x 5 = 20
Step2: Finally add 25 at the end of the result.
Answer=2025

Tips 2: Any 2 Digit Number
Ex: 47
Step1: Look for the nearest 10 boundary.
3 from 47 to 50
Step2: Since we went up 3 to 50, now go down 3 from 47 to 44.
Step3: Now mentally multiply 44 x 50 = 2200 - 1st answer.
Step4: 47 is 3 away from the 10 boundary 50, Square 3 as 9 - 2nd answer.
Step5: Add the first and second answer, 2200 + 9
Answer: 2209

Source: http://www.helpwithassignment.com/