What is 5 1/2⋅10 1/2 ? Enter the missing values in the solution. (1 point)

Answer 1

To calculate \( 5 \frac{1}{2} \cdot 10 \frac{1}{2} \), we'll first convert the mixed numbers to improper fractions.

1. Convert \( 5 \frac{1}{2} \): \[ 5 \frac{1}{2} = \frac{5 \cdot 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

2. Convert \( 10 \frac{1}{2} \): \[ 10 \frac{1}{2} = \frac{10 \cdot 2 + 1}{2} = \frac{20 + 1}{2} = \frac{21}{2} \]

Now, calculate the product of the two improper fractions: \[ \frac{11}{2} \cdot \frac{21}{2} = \frac{11 \cdot 21}{2 \cdot 2} = \frac{231}{4} \]

To express \( \frac{231}{4} \) as a mixed number:

1. Divide \( 231 \) by \( 4 \): \[ 231 \div 4 = 57 \quad \text{(with a remainder of 3)} \] So, \( 57 \) whole parts and the remainder of \( 3 \) gives: \[ \frac{231}{4} = 57 \frac{3}{4} \]

In summary, \[ 5 \frac{1}{2} \cdot 10 \frac{1}{2} = 57 \frac{3}{4} \]

The missing values in the solution are:

• \( 5 \frac{1}{2} = \frac{11}{2} \)
• \( 10 \frac{1}{2} = \frac{21}{2} \)
• Resulting product: \( \frac{231}{4} = 57 \frac{3}{4} \)