Final answer:
The missing fractions in the equation are 4/5 and 3/10. Through finding a common denominator and setting the numerators equal to each other, we determine the values to fill in the blanks and create a true equation.
Step-by-step explanation:
To solve for the missing fractions in the equation ___/5 - 1/2 = 3/___, we need to first identify a common denominator for the fractions on the left-hand side of the equation.
The least common denominator for 5 and 2 is 10. So, we rewrite 1/2 as 5/10 to have a common denominator with the first fraction.
The equation now looks like x/5 - 5/10 = 3/y.
Next, we need to solve for x.
To have the equation in terms of tenths, we multiply the numerator and the denominator of the first fraction by 2, giving us (2x)/10 - 5/10 = 3/y.
Combining the fractions on the left yields (2x - 5)/10 = 3/y.
If 3/y is equal to this fraction, then 3 times the scale factor of y must be 2x - 5.
Since we want the equation to be true when the fractions are equivalent, we set the numerators equal to each other: 2x - 5 = 3, and solve for x, giving us x = 4.
For the second blank (y), we can use the fact that the fractions are equivalent to say that 10y must be equal to 2x - 5, which we found out was equal to 3. So, 10y = 3.
Dividing both sides by 10 gives us y = 3/10. Therefore, the filled-in equation is 4/5 - 1/2 = 3/(3/10).
To simplify, we can write 3/(3/10) as 3 divided by 3/10, which gives us 10, so the final equation is 4/5 - 1/2 = 3/10.