Question

5 5/6 - 3 1/3 in simplest form in fraction form

Answer 1

To subtract the mixed numbers \(5 \frac{5}{6}\) and \(3 \frac{1}{3}\), we first convert them to improper fractions.

1. Convert \(5 \frac{5}{6}\):
\[
5 \frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{30 + 5}{6} = \frac{35}{6}
\]

2. Convert \(3 \frac{1}{3}\):
\[
3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
\]

Next, we need to subtract these two improper fractions:
\[
\frac{35}{6} - \frac{10}{3}
\]

To subtract, we need a common denominator. The least common multiple of 6 and 3 is 6. We convert \(\frac{10}{3}\) to a fraction with a denominator of 6:
\[
\frac{10}{3} = \frac{10 \times 2}{3 \times 2} = \frac{20}{6}
\]

Now we can subtract:
\[
\frac{35}{6} - \frac{20}{6} = \frac{35 - 20}{6} = \frac{15}{6}
\]

Finally, we simplify \(\frac{15}{6}\):
\[
\frac{15 \div 3}{6 \div 3} = \frac{5}{2}
\]

So, the simplest form of \(5 \frac{5}{6} - 3 \frac{1}{3}\) in fraction form is:
\[
\frac{5}{2}
\]