Question

Subtract. Simplify, if possible.
7 5/12 - 5 3/4
[__] [__]/[__]

Answer 1

To subtract the mixed numbers \(7 \frac{5}{12} - 5 \frac{3}{4}\), we'll start by converting both mixed numbers to improper fractions.

1. **Convert \(7 \frac{5}{12}\) to an improper fraction:**
\[
7 \frac{5}{12} = 7 \times 12 + 5 = 84 + 5 = 89
\]
So,
\[
7 \frac{5}{12} = \frac{89}{12}
\]

2. **Convert \(5 \frac{3}{4}\) to an improper fraction:**
\[
5 \frac{3}{4} = 5 \times 4 + 3 = 20 + 3 = 23
\]
So,
\[
5 \frac{3}{4} = \frac{23}{4}
\]

3. **Now we need to find a common denominator to subtract these fractions. The least common denominator (LCD) of 12 and 4 is 12.**

4. **Convert \(\frac{23}{4}\) to have a denominator of 12:**
\[
\frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12}
\]

5. **Now we can perform the subtraction:**
\[
\frac{89}{12} - \frac{69}{12} = \frac{89 - 69}{12} = \frac{20}{12}
\]

6. **Simplify \(\frac{20}{12}\):**
The greatest common divisor (GCD) of 20 and 12 is 4. So we divide both the numerator and denominator by 4:
\[
\frac{20 \div 4}{12 \div 4} = \frac{5}{3}
\]

7. **Convert \(\frac{5}{3}\) back to a mixed number:**
\[
\frac{5}{3} = 1 \frac{2}{3}
\]

So, \(7 \frac{5}{12} - 5 \frac{3}{4} = 1 \frac{2}{3}\).

The final answer in the format requested is:
**1** **2**/**3**.