Could someone please help me with this problem I just do not get it.
Arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals exactly 1/3 (one third)?
Example that doesn't work: 7192/38456 = 0.187
5832/17496 = 1/3.
Could someone explain HOW you get the answer I want to make sure I understand.
Sure, I can help you with this problem. It involves arranging the numerals 1 to 9 in a single fraction that equals exactly 1/3. Let's break it down step by step to find a solution.
To start with, let's think about the fraction 1/3. When we simplify this fraction, we get the numerator (top number) as 1 and the denominator (bottom number) as 3. Therefore, we need to find a way to arrange the numerals 1 to 9 such that the resulting fraction has a numerator of 1 and a denominator of 3.
To arrange these numerals, we need to consider the properties of fractions. A fraction represents a part of a whole. In our case, the whole is divided into three equal parts (denominator is 3), and we want to find the arrangement that represents one of those parts (numerator is 1).
Let's examine the properties of the numerals 1 to 9. The sum of all these numerals from 1 to 9 is 45 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45). However, the sum of our desired numerator and denominator is 4 (1 + 3 = 4). This means that the sum of the remaining numerals will be the remaining part of the whole, which is 45 - 4 = 41.
Since we are looking for a fractional representation of 1/3, our denominator is fixed at 3. So we need to find a combination of the remaining numerals, 41, that has a sum divisible by 3, and would give us a numerator of 1 when added with 1.
Let's try to arrange the numerals in descending order: 9, 8, 7, 6, 5, 4, 3, 2, 1.
Starting from the largest numeral, 9, we add it to our numerator: 1 + 9 = 10. Since 10 is not divisible by 3, we move on to the next numeral.
Next, we add 8 to our numerator: 1 + 8 = 9. Again, 9 is not divisible by 3, so we continue.
Continuing this process, we eventually reach the numeral 4. Adding 4 to our numerator: 1 + 4 = 5. This time, the sum (5) is divisible by 3 because 5 divided by 3 gives a remainder of 2.
Finally, we add the remaining numerals (3, 2, 1) to our fraction, which leaves us with 41. The resulting fraction is 5/41.
To summarize, the fraction 5/41, with the numerals arranged as 95238146/123456789, represents 1/3.
It's important to note that this problem is more of a mathematical curiosity and does not have any practical applications. The solution involves trial and error, and there is no general method for solving it.