A certain number is added to the numerator and subtracted from the denominator of 5/8. The new number equals the reciprocal f 5/8.Find the number
(5+x)/(8-x) = 8/5
all those symmetrically placed 5's and 8's make me think of x=3, without even doing the math.
See whether I'm right.
Let's assume the number we are looking for to be 'x'.
According to the given information,
New numerator = 5 + x
New denominator = 8 - x
The reciprocal of 5/8 is 8/5.
Therefore, the equation can be formed as:
(5 + x) / (8 - x) = 8/5
To solve the equation, we can cross-multiply:
5(8 - x) = 8(5 + x)
Let's simplify it step-by-step:
40 - 5x = 40 + 8x
Now, let's isolate the 'x' term:
40 - 40 = 8x + 5x
0 = 13x
To find 'x', divide both sides of the equation by 13:
0 ÷ 13 = 13x ÷ 13
0 = x
Therefore, the number we are looking for is x = 0.
To find the number that needs to be added to the numerator and subtracted from the denominator of 5/8, we can break down the problem step by step.
Let's assume the number we need to find is represented by "x". According to the problem, the new fraction should be equal to the reciprocal of 5/8.
The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of 5/8 is 8/5.
Now we can set up the equation using the information we have:
(5 + x) / (8 - x) = 8 / 5
To solve for "x", we can cross-multiply:
5(8 - x) = 8(5 + x)
40 - 5x = 40 + 8x
Now, simplify the equation:
-5x - 8x = 40 - 40
-13x = 0
Divide both sides of the equation by -13:
x = 0
Therefore, the number that needs to be added to the numerator and subtracted from the denominator of 5/8 to obtain the reciprocal 8/5 is 0.