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Showing posts with label Shortcut Techniques for multiplication with the numbers ending with 5. Show all posts
Showing posts with label Shortcut Techniques for multiplication with the numbers ending with 5. Show all posts

Wednesday, 21 August 2013

Shortcut Techniques for multiplication with the numbers ending with 5


 Shortcut Techniques for multiplication with the numbers ending with 5

Friends, here are some shortcut techniques for multiplicating with the numbers ending with 5 shared by Mr. Hareesh Kumar. We are very thankful to him for his great support and efforts.


Multiplication With 5 :

EXAMPLES: 123458 * 5 = ?
Solution : 123458*5 = (123458/2) * 10 = 61729*10 = 617290

Example: 224569*5 = ?

Solution: 224569*5 = (224569/2) * 10 = 112284.5 * 10 = 1122845

 
Hence the pattern becomes:

X * 5 = (X/2) * 10


Multiplication with 15:

Example: 124*15 =?

Solution: 124*15 = (124 + (124/2)) * 10

                                   = (124 + 62) * 10 = 1860

Hence the pattern becomes:

X*15 = (X + X/2) * 10 è X*15 = (3X/2) * 10


Multiplication with 25:

Example: 2264 * 25 =?

Solution: 2264*25 = (2264/4) * 100 = 566 * 100 = 56600

Hence the pattern is:

X*25 = (X/4)*100


Multiplication with 35:

Example: 127*35 =?

Solution: 127*35 = (3*127 + (127/2)) * 10

                             = (381 + 63.5) * 10 = 4445

Hence the pattern is:

X*35 = (3*X + X/2) * 10 è X*35 = (7X/2) * 10


Note : The above shown patterns will continue for all the numbers ending with 5. In general we can write this as:

X*n5 = (n*X + X/2) * 10


           Where, n = 0,1,2,3, ………………………………


Some more examples :   
  •  136 * 65 = (6*136 + 136/2) * 10 = (816+68)*10 = 8840 
  • 132*105 = (10*132 + 132/2) * 10 = (1320 + 66)*10 = 13860 
  •  123*55 = (5*123 + 123/2)*10 = (615+61.5)*10 = 6765

Multiplication of Numbers Ending with 5 and having the difference of 10 : 

Let us assume that there are two numbers X5 and Y5, and the difference between the two numbers is 10. 
Then the multiplication of these two numbers will be :
                 (Larger number of X and Y)2 – 1 | 75

Note : X and Y may be single digit or 2-digit or 3-digit numbers!

EXAMPLES:
1)    35*45 =?
Sol: 35*45 = (42 – 1) |75 = 1575

2)    75*85 = ?
Sol: 75*85 = (82 – 1)|75 = 6375

3)    105*115 = ?
Sol: 105*115 = (112 – 1)|75 = 12075

4)    235*245 = ?
Sol: 235*245 = (242 – 1)|75 = 57575

5)    255*245 = ?
Sol: 255*245 = (252 – 1)|75 = 62475

6)    1055*1045 = ?
Sol: 1055*1045 = (1052 – 1)|75 = 1102475

7)    1125*1135 = ?
Sol: 1125*1135 = (1132– 1)|75 = 1276875
06:26 - By Unknown 0

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