for each part, use all of the digits 5 6 7 8 9 once each and no other digits. show working to explain your answers.
what is the largest positive integer you can make from a calculation using only subtraction?
--------------------------
I was confused as to how to answer this question - do I use the numbers once each in the entire equation (e.g. 567 - 89), or am I just not allowed to repeat them in the same number? (e.g. 98765 - 56789)
If I interpret your question correctly, ...
since all the digits have to be used, we will simply subtract the smallest
possible from the largest remaining, that is
9876 - 5 = 9871
thank you!
To find the largest positive integer using only subtraction, we can use the numbers 5, 6, 7, 8, and 9 once each in the entire equation. We want to create a calculation where the difference between two numbers is maximized.
To start, let's arrange the numbers in descending order: 98765.
Now, let's subtract the smallest number we can form using these digits: 56789.
Performing the subtraction:
98765
- 56789
---------
To subtract the ones column, we borrow from the tens column:
Borrowing:
15
- 9
------
Subtracting:
15
- 9
------
6
Moving to the tens column:
78
- 89
-------
Subtracting:
78
- 89
-------
-11
Moving to the hundreds column:
8
- 6
-----
Subtracting:
8
- 6
-----
2
Moving to the thousands column:
9
- 5
-----
Subtracting:
9
- 5
-----
4
Moving to the ten-thousands column:
n/a
- 7
------
Since we ran out of digits for the ten-thousands column, we cannot continue the subtraction. Therefore, the largest positive integer we can make from a calculation using only subtraction with the digits 5, 6, 7, 8, and 9 once each is:
98765 - 56789 = 41976
So, 41976 is the largest positive integer we can create using these digits and only subtraction.
To find the largest positive integer you can make from a calculation using only subtraction, you need to use each digit (5, 6, 7, 8, 9) once and no other digits.
Let's start by considering the largest possible 5-digit number using these digits, which would be 98765. Subtracting from it would give the smallest possible result. However, this does not fulfill the requirement of using each digit once, so we need to find a different approach.
To create a larger number while still meeting the requirement, we can use the digit 8 as the first digit of our result. This means we need to subtract a 4-digit number from 8XXXX. But to maximize the result further, we need to choose the largest possible 4-digit number.
The largest possible 4-digit number using the remaining digits (5, 6, 7, 9) would be 9765. So our calculation becomes: 8765 - 9765.
Now, let's verify if this is indeed the largest possible result. We can try to subtract a larger 4-digit number (e.g., 9657) from 8765, but this would require repeating the digit 6, which is not allowed.
Calculating 8765 - 9765, we get the result of -1000. However, the question asks for the largest positive integer, so we consider the absolute value of -1000, which is 1000.
Therefore, the largest positive integer you can make from a calculation using only subtraction, using each digit 5, 6, 7, 8, 9 once and no other digits, is 1000.