# Solving Problems with Percents

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This document clearly explains the process for solving simple questions (and simple word problems) involving percents of the form:

What is 15% of 28?
What percent is 12 of 84?
16 is 10% of what number?

It is intended to be self-explanatory for students, but could also be used by teachers/parents who are teaching this topic.

This lesson explains that "percent / 100 = part / total" to show how to set up a ratio from given information, cross-multiply, and then to solve for the variable in a one step equation. (Corresponding instructional notes for Cross-Multiplying and Solving One-Step Equations are available as free downloads in my store to complement this lesson.)

In addition to the explanations, this document includes some sample questions first unsolved for student practice, then repeated with solutions so students can check their work. It also includes three completely solved and annotated word problems involving percentages. All solutions clearly demonstrate the use of "percent / 100 = part / total" to organize the given information and work through to a final answer.

While this approach may not always be the quickest method to solve basic problems, it has the advantage of not confusing students with three different calculations depending on which piece of information is missing. I have found this method to be most successful when teaching students because of its consistency and universal application. Once students are comfortable that they can solve any question with one easy method, then we explore tricks, patterns and shortcuts.

Subsequent lessons (coming soon!) address when you might choose to use some of the quicker methods as well as applying these techniques to more complicated questions involving topics such as repeated percents, multi-step problems, and percent increase/decrease.

Note: This is an 8-page, typed, updated version of an older document that was handwritten on a tablet PC and uses colour to assist in the explanations. Although the colour is extremely helpful for showing how given information is substituted into the ratio, the file can be reproduced in black and white and is still useful. The original, handwritten pages (additional 7 pages) have been included in the 2013 revision because some people do like the visual presentation of the tablet PC version. Both are provided for your convenience.
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8 + 7
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