To solve the equation ( y - 4 \frac{3}{4} = 12 \frac{3}{8} ), we first convert the mixed numbers into improper fractions.
Convert ( 4 \frac{3}{4} ):
[
4 \frac{3}{4} = 4 \times 4 + 3 = 16 + 3 = 19/4
]
Convert ( 12 \frac{3}{8} ):
[
12 \frac{3}{8} = 12 \times 8 + 3 = 96 + 3 = 99/8
]
Now, substitute these values back into the equation:
[
y - \frac{19}{4} = \frac{99}{8}
]
Next, to isolate ( y ), add (\frac{19}{4}) to both sides. We will need a common denominator to add the fractions. The common denominator of 4 and 8 is 8.
Convert (\frac{19}{4}) into eighths:
[
\frac{19}{4} = \frac{19 \times 2}{4 \times 2} = \frac{38}{8}
]
Now we can rewrite the equation:
[
y - \frac{38}{8} = \frac{99}{8}
]
Add (\frac{38}{8}) to both sides:
[
y = \frac{99}{8} + \frac{38}{8} = \frac{99 + 38}{8} = \frac{137}{8}
]
Thus, the solution is:
[
y = \frac{137}{8}
]
If you want to convert this back to a mixed number:
[
\frac{137}{8} = 17 \frac{1}{8}
]
So, the final answer is:
[
y = 17 \frac{1}{8}
]
