In the fraction 7/12, which number is the numerator and what general role does it play?

Express the improper fraction 9/4 as a mixed number and state how many whole shapes (each divided into fourths) would be fully shaded when representing 9/4 visually.

A cookie recipe calls for 3/4 cup of sugar. You mistakenly add exactly half the required amount. What fraction of the required sugar did you actually add?

Simplify 462/210 fully by using prime factorization and canceling common prime factors.

Why is it invalid to have a fraction with denominator equal to zero (for example, a/0)?