Question

Subtract. Simplify, if possible.
6 1/2 - 1 5/6 = [__] [__]/[__]

Answer 1

To subtract the mixed numbers \( 6 \frac{1}{2} \) and \( 1 \frac{5}{6} \), we can follow these steps:

1. Convert the mixed numbers to improper fractions.

For \( 6 \frac{1}{2} \):
\[
6 \frac{1}{2} = 6 \cdot 2 + 1 = 12 + 1 = 13 \quad \Rightarrow \quad \frac{13}{2}
\]

For \( 1 \frac{5}{6} \):
\[
1 \frac{5}{6} = 1 \cdot 6 + 5 = 6 + 5 = 11 \quad \Rightarrow \quad \frac{11}{6}
\]

2. Now, we must subtract:
\[
\frac{13}{2} - \frac{11}{6}
\]

3. To perform the subtraction, we need a common denominator. The least common multiple of 2 and 6 is 6. We convert \( \frac{13}{2} \) to have a denominator of 6:
\[
\frac{13}{2} = \frac{13 \cdot 3}{2 \cdot 3} = \frac{39}{6}
\]

4. Now we can subtract:
\[
\frac{39}{6} - \frac{11}{6} = \frac{39 - 11}{6} = \frac{28}{6}
\]

5. Finally, simplify \( \frac{28}{6} \):
\[
\frac{28}{6} = \frac{14}{3} \quad \text{(by dividing both numerator and denominator by 2)}
\]

6. Convert \( \frac{14}{3} \) back to a mixed number:
\[
14 \div 3 = 4 \quad \text{with a remainder of } 2, \text{ so } 4 \frac{2}{3}
\]

Thus, the answer is:
\[
4 \frac{2}{3} = 4 \quad 2 \quad 3
\]

The final answer is:
\[
[4] [2]/[3]
\]