Questions: Find the indicated difference. Express your answer in mixed number form, and reduce if possible. 46 4/11 - 11 5/11

Solution Steps

To solve the subtraction of mixed numbers, we need to follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Subtract the improper fractions.
3. Convert the result back to a mixed number.
4. Simplify the mixed number if possible.

First, we convert the mixed numbers to improper fractions: \[ 46 \frac{4}{11} = \frac{46 \times 11 + 4}{11} = \frac{506 + 4}{11} = \frac{510}{11} \] \[ 11 \frac{5}{11} = \frac{11 \times 11 + 5}{11} = \frac{121 + 5}{11} = \frac{126}{11} \]

Next, we subtract the improper fractions. Since the denominators are the same, we can directly subtract the numerators: \[ \frac{510}{11} - \frac{126}{11} = \frac{510 - 126}{11} = \frac{384}{11} \]

We convert the improper fraction \(\frac{384}{11}\) back to a mixed number: \[ \frac{384}{11} = 34 \frac{10}{11} \] This is because: \[ 384 \div 11 = 34 \quad \text{remainder} \quad 10 \] So, we have: \[ 34 \frac{10}{11} \]

The fraction \(\frac{10}{11}\) is already in its simplest form since the greatest common divisor (GCD) of 10 and 11 is 1.

Final Answer