How is the mixed number 10 1/2 written as an improper fraction?

To convert a mixed number to an improper fraction, the process involves multiplying the whole number part by the denominator of the fractional part, then adding the numerator of the fractional part, and placing this result over the original denominator.

In this case, the mixed number is 10 1/2. The whole number part is 10 and the fractional part is 1/2.

1. First, multiply the whole number (10) by the denominator of the fractional part (2):

( 10 \times 2 = 20 ).

2. Next, add the numerator of the fractional part (1) to this result:

( 20 + 1 = 21 ).

3. Finally, place this result over the original denominator:

This gives ( \frac{21}{2} ).

Thus, the mixed number 10 1/2 is correctly expressed as the improper fraction 21/2. This conversion is standard practice in mathematics and is particularly useful for simplifying calculations or in scenarios where the denominator needs to be uniform.