Question

What is the difference of 3 and 1/2
and 1 and 2/3
(1 point)

Answer 1

To find the difference between \( 3 \frac{1}{2} \) and \( 1 \frac{2}{3} \), we first convert the mixed numbers to improper fractions.

1. Convert \( 3 \frac{1}{2} \):
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]

2. Convert \( 1 \frac{2}{3} \):
\[
1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
\]

Next, we find the difference:
\[
\frac{7}{2} - \frac{5}{3}
\]

To subtract these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6.

Convert both fractions:
\[
\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}
\]
\[
\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
\]

Now subtract:
\[
\frac{21}{6} - \frac{10}{6} = \frac{21 - 10}{6} = \frac{11}{6}
\]

Thus, the difference of \( 3 \frac{1}{2} \) and \( 1 \frac{2}{3} \) is \( \frac{11}{6} \) or \( 1 \frac{5}{6} \) when expressed as a mixed number.

So the final answer is:
\[
\frac{11}{6} \text{ or } 1 \frac{5}{6}
\]