Prep for Calculus Notes

Math 105 - Fall 2025

We started with a 30 minute assessment pre-test that is not for a grade. After that we reviewed the rules for working with fractions.

Addition. To add fractions, they need a common denominator (bottom). Once you have a common denominator, just add the numerators (tops). We did these examples:
1. $\dfrac{1}{6} + \dfrac{2}{6}$
2. $\dfrac{1}{6} + \dfrac{2}{5}$
Multiplication. I like to say that “fractions play nice with multiplication”. To multiply fractions, just multiply the tops and multiply the bottoms.
1. $\dfrac{1}{6} \cdot \dfrac{2}{5}$
Division. Division is just multiplication by the reciprocal. You might have learned this as “keep-change-flip” or as “flip-and-multiply”.
1. $\dfrac{ ~\dfrac{1}{6}~}{~\dfrac{2}{5}~ }$
2. $\dfrac{ ~\dfrac{1}{6}~}{~5~ }$