Question

Find the difference.
4 5/9 - 3 1/3
Simplify your answer completely.
[__] [__]/[__]

Answer 1

To find the difference \( 4 \frac{5}{9} - 3 \frac{1}{3} \), we first convert the mixed numbers into improper fractions.

1. **Convert \( 4 \frac{5}{9} \)**:
\[
4 \frac{5}{9} = \frac{4 \times 9 + 5}{9} = \frac{36 + 5}{9} = \frac{41}{9}
\]

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

Now we have:
\[
4 \frac{5}{9} - 3 \frac{1}{3} = \frac{41}{9} - \frac{10}{3}
\]

3. **Find a common denominator**:
The common denominator between 9 and 3 is 9. We need to convert \(\frac{10}{3}\) to have a denominator of 9:
\[
\frac{10}{3} = \frac{10 \times 3}{3 \times 3} = \frac{30}{9}
\]

4. **Now subtract the fractions**:
\[
\frac{41}{9} - \frac{30}{9} = \frac{41 - 30}{9} = \frac{11}{9}
\]

5. **Convert \(\frac{11}{9}\) back to a mixed number**:
\(\frac{11}{9}\) can be expressed as:
\[
1 \frac{2}{9}
\]
Since \(11 \div 9 = 1\) with a remainder of \(2\).

Thus, the difference \(4 \frac{5}{9} - 3 \frac{1}{3}\) simplifies to:
\[
\boxed{1 \quad 2/9}
\]