\( ( 98 + 69 ) ( \bmod 6 ) = \square ( \bmod 6 ) \)

First, let's break it down! We need to first find the sum \( 98 + 69 \), which gives us \( 167 \). Now, we take \( 167 \bmod 6 \). To do this, we divide \( 167 \) by \( 6 \), which gives us a quotient of \( 27 \) and a remainder of \( 5 \). So, \( 167 \bmod 6 = 5 \). Therefore, \( ( 98 + 69 ) ( \bmod 6 ) = 5 \). Now, let's think about why we’re using modulo 6! Modulo operations are widely used in computer science, especially in algorithms for hashing and maintaining small numbers during calculations. They help to avoid overflow and keep numbers manageable, while still preserving essential information!