To perform the operation (10 - 7 \frac{5}{12}), start by converting the mixed number (7 \frac{5}{12}) into an improper fraction.
- Convert (7) to a fraction: (7 = \frac{7 \times 12}{12} = \frac{84}{12}).
- Add the fraction part: (7 \frac{5}{12} = \frac{84}{12} + \frac{5}{12} = \frac{89}{12}).
Now, you can perform the subtraction:
[
10 - 7 \frac{5}{12} = 10 - \frac{89}{12}
]
Convert (10) to a fraction with a denominator of (12):
[
10 = \frac{10 \times 12}{12} = \frac{120}{12}
]
Now we can subtract:
[
\frac{120}{12} - \frac{89}{12} = \frac{120 - 89}{12} = \frac{31}{12}
]
Therefore, the result of the operation is:
[
\frac{31}{12}
]
If you want to convert (\frac{31}{12}) back into a mixed number:
[
31 \div 12 = 2 \quad \text{(whole number)} \quad \text{with a remainder of } 7
]
So,
[
\frac{31}{12} = 2 \frac{7}{12}
]
Thus, (10 - 7 \frac{5}{12} = 2 \frac{7}{12}).
