Question

Subtract, answer as a mixed number in simplest form.
2 1/2 - 2 1/7
[__] [__]/[__]

Answer 1

To subtract the mixed numbers \(2 \frac{1}{2}\) and \(2 \frac{1}{7}\), we first convert them to improper fractions.

1. Convert \(2 \frac{1}{2}\):
\[
2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \text{so it becomes} \quad \frac{5}{2}
\]

2. Convert \(2 \frac{1}{7}\):
\[
2 \frac{1}{7} = 2 \times 7 + 1 = 14 + 1 = 15 \quad \text{so it becomes} \quad \frac{15}{7}
\]

3. Now we need to subtract \(\frac{5}{2}\) from \(\frac{15}{7}\). To do this, we need a common denominator. The least common multiple (LCM) of 2 and 7 is 14.

4. Rewrite each fraction with the common denominator:
- For \(\frac{5}{2}\):
\[
\frac{5}{2} = \frac{5 \times 7}{2 \times 7} = \frac{35}{14}
\]
- For \(\frac{15}{7}\):
\[
\frac{15}{7} = \frac{15 \times 2}{7 \times 2} = \frac{30}{14}
\]

5. Now we can subtract the fractions:
\[
\frac{30}{14} - \frac{35}{14} = \frac{30 - 35}{14} = \frac{-5}{14}
\]

6. Since we have a negative fraction, we can express this as a negative mixed number. The absolute value of \(-\frac{5}{14}\) is less than 1, so we keep it as is.

Thus, the final answer in mixed number form is:
\[
-\frac{5}{14}
\]

So the answer is:
\[
[0] [5]/[14]
\]

This indicates \(0\) whole, \(5\) as the numerator, and \(14\) as the denominator for the proper fraction part of the mixed number.