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Consider the following multiplication in decimal notations: (999).(abc)=def132 , determine the digits a,b,c,d,e,f.

Consider the following multiplication in decimal notations:

(999).(abc)=def132 , determine the digits a,b,c,d,e,f.

Grade:9

1 Answers

Khushpreet Singh
33 Points
8 years ago

a=8
b=6
c=8

d=8
e=6
f=7

In other words, 999 * 877 = 876132.

You don''t need to find out d,e,f, as they''re dependent. You only need to find out a,b,c.

Now, start with c, because it''s in the ones place and thus easiest. What digit, when multiplied by 9, gives a "2" in the ones? The answer: 8. because 8 * 9 = 72. That the "2" you have there.

Now we need to find out b. What digit, when multipled by 9, and added 9 (from the step above, the tens digit), gives a "4" in the ones? The naswer: 6. because 6 * 9 = 54, and added 9 to 4 gives us 13. That''s the "3" we have there. 

Now we need to find out c. what digit when multiplied with 9 and added 19 (from the step above) , gives a  "1" in the ones..? the answer :8 because 8*9 = 72 and added 2 to 19 gives 21. that''s "1" we have there

now we have a=8 , b=6 , c=8  therefore we have 999*868=def132. multiply both the numbers and you get d, e and f..

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