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