what fraction must be added to the difference of 5/6 and 2/3 to have an average of 1/4
5/6 - 4/6 = 1/6
1/6 + what = 2 (1/4)
twice because average of two things is sum over two
1/6 + what = 2/4 = 3/6
what = 2/6 = 1/3
the answer is not in the given choices
the choices are 35/2 , 40/2, 45/2
That does not make any sense to me.
i will try again on my own ,,anyway tnx for the ideas
How about this ?
(5/6 - 2/3 + x)/3 = 1/4
1/6 + x = 3/4
x = 3/4 - 1/6 = 7/12
I agree with Damon, the wording is rather ambiguous.
To find the fraction that must be added to the difference of 5/6 and 2/3, we need to determine two things:
1) The difference between 5/6 and 2/3.
2) The fraction that needs to be added to the difference to achieve an average of 1/4.
Let's calculate the difference between 5/6 and 2/3 first:
To find the difference between two fractions, you subtract the second fraction from the first. In this case, we subtract 2/3 from 5/6.
5/6 - 2/3:
Since the denominators (6 and 3) are different, we need to find a common denominator. The common denominator can be found by multiplying the two denominators together, which gives us 6 * 3 = 18.
Now, we rewrite both fractions with the common denominator of 18:
5/6 = (5/6) * (3/3) = 15/18
2/3 = (2/3) * (6/6) = 12/18
Now we can subtract the two fractions:
15/18 - 12/18 = (15 - 12)/18 = 3/18 = 1/6
So the difference between 5/6 and 2/3 is 1/6.
Now we need to find the fraction that needs to be added to this difference to have an average of 1/4.
Let x be the fraction to be added.
To find the average of two fractions, you add them together and then divide the sum by 2. In this case, we want the average to be 1/4.
So the equation is:
(1/6 + x)/2 = 1/4
To solve for x, we can cross-multiply:
2(1/6 + x) = 1/4
2/6 + 2x = 1/4
Multiplying both sides by 12 to eliminate fractions:
4(1/6 + x) = 12 * (1/4)
4/6 + 4x = 12/4
4/6 + 4x = 3
Now, we simplify the equation:
4x = 3 - 2/3
4x = 9/3 - 2/3
4x = 7/3
To solve for x, we divide both sides by 4:
x = (7/3) / 4
x = 7/12
Therefore, the fraction that must be added to the difference of 5/6 and 2/3 to have an average of 1/4 is 7/12.