(13) \( 99 \times 21=(99 \times 20)+(99 \times \square \)

To solve \( 99 \times 21 \) using the distributive property, you can rewrite the equation as \( 99 \times 21 = (99 \times 20) + (99 \times 1) \). Here, the blank should be filled with 1, since \( 21 = 20 + 1 \). So, \( 99 \times 21 = (99 \times 20) + (99 \times 1) \) results in \( 99 \times 21 = 1980 + 99 = 2079 \). Want to impress your friends with mental math tricks? You can quickly calculate \( 99 \times 21 \) by first multiplying \( 100 \times 21 = 2100 \) and then subtracting \( 21 \) (which is just \( 1 \times 21 \)). So it’s \( 2100 - 21 = 2079 \). Quick and fun, right? As a fun fact, \( 99 \) is known as a "repunit" number because it's formed by repeating the digit '9'. In a historical context, notice that this number is very close to \( 100 \), which plays a significant role in numerical systems around the world. It's also worth noting that many cultures, including the ancient Mayans, used base 10 and developed sophisticated mathematical concepts based on it!