HOW TO MULTIPLY ANY NUMBER BY 9 99 AND 999

In this section we will learn, how to multiply any number by 9, 99 and 999 etc.

• If we have 9, we may write it as 10 - 1
• If we have 99, we may write it as 100 - 1
• If we have 999, we may write it as 1000 - 1 etc.

Now we have to remember that, when we multiply any number by 10, 100, 1000 etc, we get the same number ends with zeroes.

For example,

57 x 10  =  570 (ends with 1 zero)

484 x 100  =  48400 (ends with two zeroes)

Let us consider the following examples to understand the concept given above.

Example 1 :

Evaluate

587 x 999  =  

(A)  586413  (B)  587523  (C)  614823  (D)  615173

Solution :

  =  587 x 999

We may write 999 as 1000 - 1.

  =  587 x (1000 - 1)

  =  587000 - 587

  =  586413

Example 2 :

Evaluate

3897 x 999  =  

(A)  3883203 (B)  3893103 (C)  3639103  (D)  3791203

Solution :

  =  3897 x 999

We may write 999 as 1000 - 1.

  =  3897 x (1000 - 1)

  =  3897000 - 3897

  =  3893103

Example 3 :

Evaluate

72519 x 9999  =  

(A)  725117481 (B)  674217481

(C)  685126481  (D)  696217481

Solution :

  =  72519 x 9999

We may write 9999 as 10000 - 1.

  =  72519 x (10000 - 1)

  =  725190000 - 72519

  =  725117481

Example 4 :

For each question below, do only the first three multiplication problems. Write out the next three product based on your conjecture.

5 x 9  = 

55 x 99  =  

555 x 999  =  

5555 x 9999  =  

55555 x 99999  =  

555555 x 999999  =   

Solution :

By analyzing the pattern, in every row, we see the increased number of 5's as well 9's.

5 x 9  = 45

55 x 99  =  55 x (100 - 1)

  =  5500 - 55

  =  5445

(one 5 at the start one 5 at the end, in the middle we have two 4's)

555 x 999  =  555 x (1000 - 1)

  =  555000 - 555

  =  554445

(Two 5's at the start one 5 at the end, in the middle  we have three 4's)

So, the number of 5's and 4's are increasing as the number of 5's and 9's are increased in the question.

5555 x 9999  =  55,544,445

55555 x 99999  =  5,555,444,445

555555 x 999999  =   555,554,444,445

Example 5 :

8 x 9  = 

88 x 99  =  

888 x 999  =  

8888 x 9999  =  

88888 x 99999  =  

888888 x 999999  =   

Solution :

By analyzing the pattern, in every row we see the increased number of 8's as well 9's.

8 x 9  =  72

88 x 99  =  88 x (100 - 1)

  =  8800 - 88

  =  8712

(one 5 at the start one 5 at the end, in the middle two 4's)

888 x 999  =  888 x (1000 - 1)

  =  888000 - 888

  =  887112

Number of 8's and 1's are increasing as the number of 8's and 9's are increased in the question.

8888 x 9999  =  88,871,112

88888 x 99999  =  8,888,711,112

888888 x 999999  =   888,887,111,112

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