Final answer:
To solve for the number, an equation is set up based on the difference of the reciprocal of the unknown number and (7/30) being (4/15). Through finding a common denominator and simplifying, it is determined that the unknown number is 2.
Step-by-step explanation:
The student's question involves finding a number when given the difference between the reciprocal of this number and a fraction, (7/30), is another fraction, (4/15). To solve this, we set up an equation where x represents the unknown number. The reciprocal of x is 1/x. According to the problem, the difference between 1/x and (7/30) is (4/15).
So the equation to solve is:
1/x - 7/30 = 4/15
First, we find a common denominator to combine the fractions, which is 30x. The equation becomes:
30 - 7x = (8/15)30x
Simplify and solve for x:
30 - 7x = 8x
Combine like terms:
30 = 15x
Divide both sides by 15 to isolate x:
x = 2
Thus, the number we are looking for is 2.