Powerful Patterns 7: Multiplying Specific Numbers by 5
Look at the list in the virtual chalkboard below. You should notice a pattern...
9 × 5 = 45
99 × 5 = 495
999 × 5 = 4,995
9,999 × 5 = 49,995
99,999 × 5 = 499,995
999,999 × 5 = 4,999,995
When a 9 is added to the multiplicand, a 9 is added to the product between the 4 & 5! Notice that the product has 1 9 fewer than the multiplicand each time!
Look out, because here comes another list with a similar pattern just below!
7 × 5 = 35
77 × 5 = 385
777 × 5 = 3,885
7,777 × 5 = 38,885
77,777 × 5 = 388,885
777,777 × 5 = 3,888,885
When a 7 is added to the multiplicand, an 8 is added to the product between the 3 & 5! There are no 8's when there's just 1 7 in the multiplicand, but
when there are 2 7's or more, there are 8's in the product! However, when there are 4 7's in the multiplicand for example, there are 3 8's in the product!
(The number of 8's is 1 fewer than the number of 7's!)
Again, Dottie Doll asks you this question:
Here's another list with a pattern like this!
2 × 5 = 10
22 × 5 = 110
222 × 5 = 1,110
2,222 × 5 = 11,110
22,222 × 5 = 111,110
222,222 × 5 = 1,111,110
In this one, when a 2 is added to the multiplicand, a 1 is added to the product! There are as many 1's in the product as there are 2's in the multiplicand!
There's 1 more list with a pattern like this!
3 × 5 = 15
33 × 5 = 165
333 × 5 = 1,665
3,333 × 5 = 16,665
33,333 × 5 = 166,665
333,333 × 5 = 1,666,665
When a 3 is added to the multiplicand, a 6 is added to the product between the 1 & 5! There are no 6's when there's just 1 3 in the multiplicand, but
when there are 2 3's or more, there are 6's in the product! However, when there are 4 3's in the multiplicand for example, there are 3 6's in the product!
(The number of 6's is 1 fewer than the number of 3's!)
The exact same digit is repeated in these multiplicands! The digits that I put in the multiplicands in each example respectively are 9, 7, 2 & 3. Try this math trick with the other digits & see what patterns you get in
the products! And remember to multiply by 5!
Wait a minute! I just remembered: Zero(0) multiplied by any number is still zero! But anyway, the other digits to try are 1, 4, 5, 6, & 8.
Speaking of patterns, maybe you already seen some other numerical math patterns that other mathematicians already discovered & published! (Besides me or you; any open-minded person can be a great mathematician, like me!)
Back to Index Page Back to Math Trick Menu
© Derek Cumberbatch