Question

Subtract. Simplify, if possible.
6 1/6 - 1 1/3
[__] [__]/[__]

Answer 1

To subtract the mixed numbers \(6 \frac{1}{6}\) and \(1 \frac{1}{3}\), we will first convert them into improper fractions.

1. Convert \(6 \frac{1}{6}\) to an improper fraction:

\[
6 \frac{1}{6} = 6 \times 6 + 1 = 36 + 1 = 37 \quad \text{(so, it becomes } \frac{37}{6} \text{)}
\]

2. Convert \(1 \frac{1}{3}\) to an improper fraction:

\[
1 \frac{1}{3} = 1 \times 3 + 1 = 3 + 1 = 4 \quad \text{(so, it becomes } \frac{4}{3} \text{)}
\]

3. Now we need to subtract \(\frac{4}{3}\) from \(\frac{37}{6}\). To do this, we need a common denominator. The least common multiple of 6 and 3 is 6.

4. Convert \(\frac{4}{3}\) to have a denominator of 6:

\[
\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}
\]

5. Now we can perform the subtraction:

\[
\frac{37}{6} - \frac{8}{6} = \frac{37 - 8}{6} = \frac{29}{6}
\]

6. We can convert \(\frac{29}{6}\) back to a mixed number:

Since \(29 \div 6 = 4\) with a remainder of \(5\), we can express it as:

\[
\frac{29}{6} = 4 \frac{5}{6}
\]

Thus, the final answer is:

\[
\boxed{4} \quad \boxed{5} \quad \boxed{6}
\]