How do you find this...
"When you multiply 2178 by 4, the product is 8712.
Notice that the digits in the product are the reverse of the digits in 2178. Find the four digit number whose digits are reversed when multiplied by nine."
2007-09-11 12:36:24 · 14 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
it has to be 4 digits and 18 times 9 is not 81...
2007-09-11 12:45:09 · update #1
1089 * 9 = 9801.
My reasoning is:
1) The number to be multiplied must start with a one, if the product will remain 4 digits if multiplied by 9.
2) The last digit of the number to be multiplied must end with a 9, since the product would have to begin with 9.
3) The sum of the digits must be equal to a number that is divisible by 9, since the product is divisible by nine. So I inserted an 8 to make 1+9+8=18.
2007-09-11 12:45:20 · answer #1 · answered by SoulDawg 4 UGA 6 · 1⤊ 1⤋
Ok.. start by narrowing down the search... You can do this completely logically without the need for trial and error (ie putting random four digit numbers into a calculator, like some here have done)
You know its a 4 digit number, and when multiplied by 9, it is the same numbers in reverse order. That implies that it is also a 4 digit muber, so the minimum value is 1000 and the maximum value is 9999.
But we can narrow it down further than that. Since you have to multiply a four digit number by 9 and get a four digit number, the higher number is between 9000 and 9999, and the lower number between 1000 and 1111, so we only have 111 numbers left now.
Secondly, we know that it is a multiple of 9. There is a rule that if you add up all the digits in ta multiple of 9, then they add up to 9:
eg
2178 is a multiple of 9 because:
2+1+7+8 = 18, 1+8 = 9
so, all the numbers between 1000 and 1111 that add up to 9 are:
1008, 1017, 1026, 1035, 1044, 1053, 1062, 1071, 1080, 1089, 1098, and 1107
Next, you can either plug these into a calculator and do it by trial and error, or you can use another hint:
You know that the higher number has to start with a 9 (because of our first clue), and thus the lower number must END with a 9, and in this list, there is only one number that does that... 1089.
so, try it in your calculator and you find that indeed:
1089 * 9 = 9801
2007-09-11 19:54:15 · answer #2 · answered by Richard W 4 · 0⤊ 0⤋
The answer is 1089.
Because, 1089 * 9 = 9801.
This is how I found it.
I tried different numbers and found that the first number had to be 1 and the second had to be 0. Otherwise, the number was over 10,000 and not four digits.
Then I realized that the last digit had to be 9, since the answer had to start with 9.
So the number was 10_9. I just tried numbers until I got 8.
2007-09-11 19:45:24 · answer #3 · answered by Larry C 3 · 1⤊ 1⤋
because its four digits,and the reverse is also 4digits, the first digit has to be 1 and the last 9,and the second can only be 0 or 1.
1109*9=9981
1119*9=11071so the second digit cant be 1 so its zero,and a little trial and error can solve the rest.
1009*9=9081
1019*9=9171
1029*9=9261
1039*9=9351
1049*9=9441
1059*9=9531
1069*9=9621
1079*9=9711
1089*9=9801
and theres ur answer
2007-09-11 19:51:44 · answer #4 · answered by vIcToR 1 · 2⤊ 1⤋
1089 x 9 = 9801
2007-09-11 19:51:33 · answer #5 · answered by Anonymous · 0⤊ 2⤋
1089 * 9 = 9801
2007-09-11 19:50:36 · answer #6 · answered by ANNAGINA M 2 · 0⤊ 2⤋
That's great that the answer is 1089*9, but how do you figure it out?
2007-09-11 19:47:54 · answer #7 · answered by Hesher 2 · 0⤊ 3⤋
Hey im in 7th too! sorry cant help ya there we are studying variables and equasions and since math is my weakest subject i dont wanna give u a wrong answer...Good luck tho...(and if no one can help just tell your teacher tomorrow u had trouble with that one...Works for me ;)
2007-09-11 19:44:30 · answer #8 · answered by Anonymous · 1⤊ 2⤋
1089.
2007-09-11 19:51:58 · answer #9 · answered by bdc3141 4 · 0⤊ 3⤋
1111 x9 =9999 thats the best i can do lol
2007-09-11 19:55:08 · answer #10 · answered by Debby 2 · 0⤊ 1⤋