Can you 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)?
Could someone explain how you get the answer to the problem, please don't just say the answer!
Yes, it is possible to arrange the numerals 1 to 9 in a single fraction that equals exactly 1/3. Here's the step-by-step process:
1. Begin by setting up the fraction with three digits in the numerator and three digits in the denominator:
1 _ _
__ __
2. To achieve 1/3, the numerator's sum should equal the denominator, and all digits from 1 to 9 should be used once. Since 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 equals 45, the denominator should be 45.
3. We can start by trying a few possibilities for the numerator. Let's consider the simplest option first:
1 _ _
__ 4 5
4. Based on the numerator's sum, we need to figure out which two digits should fill in the remaining blanks. Since 1 + 2 + 3 equals 6, there are still 39 units left in the denominator.
5. Now, let's try placing 2 in the second slot of the numerator:
1 2 _
__ 4 5
6. To calculate what goes in the third slot of the numerator, we need to find a number that sums up to 39 when combined with 3.
By trying different combinations, we find 8 + 9 equals 17, and 4 + 5 + 6 equals 15. Adding those two sums together equals 32, which is still short of 39. Thus, finding a solution with the first digit as 2 is not possible.
7. Let's go back to step 4 and try another possibility. Instead of placing 2 in the second slot of the numerator, let's try 3:
1 3 _
__ 4 5
8. Now, we need to find a number that sums up to 39 when combined with 2 (the third digit) in the numerator.
By trying different combinations, we find 7 + 8 + 9 equals 24. Subtracting 24 from 39 equals 15, so we still need 15 units.
9. We can fill in the remaining digits (2, 4, 5, 6) in any order in the numerator. Let's try the following arrangement:
1 3 5
__ 4 2
10. Now we have to calculate the value of the fraction 135/425. If we perform the division, we find that it is equal to 0.3176, which is not equal to 1/3.
11. Therefore, the arrangement 1 3 5 / 4 2 does not satisfy the condition. It means that there is no possible arrangement of the digits 1 to 9 that can form a fraction equal to 1/3.
To find a fraction that equals exactly 1/3 using the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8, and 9), we can approach this problem step by step.
First, let's observe that a fraction can be written as the numerator divided by the denominator. In this case, we want our fraction to equal 1/3.
We have nine numerals available to us, so we can try placing these numerals in different positions to form different fractions.
Let's consider some possible combinations of placing the numerals in the numerator and denominator:
1. Placing a single numeral in both the numerator and denominator:
For example, if we put the numeral 3 in both the numerator and denominator, we would have 3/3. However, this is equal to 1, not 1/3.
2. Placing two numerals in the numerator and one numeral in the denominator:
For example, if we put the numerals 1 and 2 in the numerator, and the numeral 3 in the denominator, we would have (1 + 2) / 3 = 3 / 3 = 1. This is again equal to 1, not 1/3.
3. Placing one numeral in the numerator and two numerals in the denominator:
For example, if we put the numeral 3 in the numerator, and the numerals 1 and 2 in the denominator, we would have 3 / (1 + 2) = 3 / 3 = 1. Still, this is equal to 1, not 1/3.
After exploring various combinations, you will find that it is not possible to arrange the numerals 1 to 9 in a single fraction that equals exactly 1/3 (one third). It is essential to understand that there may be multiple approaches to a problem, so feel free to explore and try different combinations yourself.