Question

Is the product of 13 1/4 x 26 1/4
greater than, less than, or equal to 13 1/4? Show you are correct by calculating the product.

Answer 1

To determine whether the product of \( 13 \frac{1}{4} \) and \( 26 \frac{1}{4} \) is greater than, less than, or equal to \( 13 \frac{1}{4} \), we need to calculate the product.

First, let's convert these mixed numbers to improper fractions.

1. Convert \( 13 \frac{1}{4} \):
\[
13 \frac{1}{4} = 13 \times 4 + 1 = 52 + 1 = 53
\]
So, \( 13 \frac{1}{4} = \frac{53}{4} \).

2. Convert \( 26 \frac{1}{4} \):
\[
26 \frac{1}{4} = 26 \times 4 + 1 = 104 + 1 = 105
\]
So, \( 26 \frac{1}{4} = \frac{105}{4} \).

Now, we can calculate the product:
\[
\text{Product} = \left( \frac{53}{4} \right) \times \left( \frac{105}{4} \right) = \frac{53 \times 105}{4 \times 4} = \frac{5565}{16}.
\]

Next, let's convert \( \frac{5565}{16} \) back to a mixed number to compare it with \( 13 \frac{1}{4} \).

To do this, we divide:
\[
5565 \div 16 = 347 \quad \text{(with a remainder)}
\]
Calculating the exact remainder:
\[
16 \times 347 = 5552,
\]
So,
\[
5565 - 5552 = 13.
\]
This means:
\[
\frac{5565}{16} = 347 \frac{13}{16}.
\]

Now we compare \( 347 \frac{13}{16} \) with \( 13 \frac{1}{4} \):
- \( 13 \frac{1}{4} = 13.25 \)
- \( 347 \frac{13}{16} \) equals \( 347 + 0.8125 = 347.8125 \).

Clearly, \( 347.8125 \) is much greater than \( 13.25 \).

Thus, the product \( 13 \frac{1}{4} \times 26 \frac{1}{4} \) is greater than \( 13 \frac{1}{4} \).

**Final conclusion**: The product of \( 13 \frac{1}{4} \times 26 \frac{1}{4} \) is greater than \( 13 \frac{1}{4} \).