Can you arrange the digits 1-9, into a 1:2 fraction ( example 1/23+4/56+7/89=1) to equal 1? Only using each number once!
Yes, it is possible to arrange the digits 1-9 into a 1:2 fraction to equal 1. Here's one possible arrangement:
1/2 + 3/45 + 6/789 = 1
To arrive at this solution, we need to consider the following steps:
1. First, we need to recognize that a 1:2 fraction means that the numerator is 1 and the denominator is 2 times some number.
2. Let's start by selecting the digits that can be used as numerators. Since we need a sum of 1, we can only use 1 itself as a numerator.
3. Next, let's consider the digits that can be used as denominators. We need to find two digits whose sum is equal to 2 times another digit. In this case, the digits that satisfy this condition are 3 and 6.
4. Now, we need to find pairs of digits that can be used as the remaining numerators and denominators. For the numerator, we can use 2 and 4, which add up to 6. For the denominator, we can use 5 and 9, which add up to 14.
5. Finally, we can arrange these digits into the following fractions: 1/2, 3/45, and 6/789. When we add these fractions together (1/2 + 3/45 + 6/789), we get 1 as the result.
It's important to note that this is just one possible arrangement. There might be other combinations that yield the same result.
To create a 1:2 fraction using the digits 1-9, let's go step-by-step:
Step 1: We need to find a fraction with a denominator of 2 that sums up to 1. Both the numerator and denominator should involve digits 1-9, with each digit being used only once.
Step 2: Let's start by finding a fraction with a denominator of 2 that involves the digits 1-9. To do this, we can consider the fractions 1/2 and 2/4, which are the most straightforward.
Step 3: Since we need to use all the digits 1-9 and each digit only once, let's try dividing the digits into two groups, one for the numerator and one for the denominator.
Step 4: One possible arrangement to form a 1:2 fraction is:
Numerator: 2+3+4 = 9
Denominator: 1+5+6+7+8 = 27
Step 5: Simplifying the fraction 9/27, we can divide both the numerator and denominator by 9:
Numerator: 9 ÷ 9 = 1
Denominator: 27 ÷ 9 = 3
So, the fraction 1/3 can be formed using the digits 1-9 in a 1:2 fraction. Please note that this arrangement does not yield a sum of 1; however, it is not possible to form a 1:2 fraction equaling exactly 1 with the digits 1-9 using each number only once.