Suppose that one number contains the same digit as another number, but in resverse order. What is true about the difference of the two number?
i need help
I don't get the question. Two different numbers share a digit. "But in reverse order"? What does reverse order mean? What is being reversed?
as in 346 and 643
The difference will always be divisible by 9.
we can work with a 4-digit number, but the logic works for any number of digits. If the digits are
a,b,c,d then the value is
abcd = 1000a+100b+10c+d
dcba = 1000d+100c+10b+a
abcd-dcba =
999a + 90b - 90c - 999d
To find out what is true about the difference of two numbers that contain the same digit but in reverse order, let's consider an example. Let's say we have two numbers: ABC and CBA, where A, B, and C represent digits.
To find the difference between these two numbers, we subtract the smaller number from the larger number. So, the difference is:
CBA - ABC
Let's break down the calculation:
CBA - ABC = (C x 100) + (B x 10) + A - (A x 100) - (B x 10) - C
Simplifying, we get:
(C x 100 + B x 10 + A) - (A x 100 + B x 10 + C)
We can observe that the result is independent of the values of A, B, and C. This means that, regardless of the specific digits chosen for A, B, and C, the difference will always be the same for two numbers that contain the same digits but in reverse order. The result is always 0.