# Solving Problems Using Percents - more examples

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FRESHLY UPDATED IN 2014!

This document explains how several "more complicated" word problems involving percents can actually be reduced to simpler questions by ensuring that you are trying to solve a problem 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/tutors who are teaching this topic.

This lesson follows "Solving Problems Using Percents" which tackled one of my personal pet peeves as a math tutor: teachers and instructional materials that make questions about percents so darn complicated! I have seen teachers require that students memorize and use three separate formulas for answering these questions. Why do this when just one method, requiring only cross multiplication and solving a one-step equation will do?

This lesson solves more complicated word problems always using "percent / 100 = part / total" to show how to set up a ratio from given information and then to solve for the variable in a one step equation. It includes 26 completely solved and annotated word problems involving percentages.

Hints are made throughout that this method isn't always the best method to use. This method will always require setting up an equivalent ratio, cross multiplying and solving a one-step equation. Sometimes, that's more work than we really need to do. But, this method is chosen because it ALWAYS works and requires no memorization beyond "percent / 100 = part / whole" thereby requiring the least "learning curve" to actually complete the problems.

This mini-lesson suggests that you will want to also consult mini-lesson that follows it: "Percents: Beyond Cross Multiplying" (coming soon!) for specific examples of different "tricks" that you may eventually choose to employ to solve these problems more quickly and with fewer steps. It openly acknowledges that there are many cases where you'll want to use a shorter method to solve the problems, but that if you can use this method, you will never be "stuck." Some students will want this as a "back up/last resort" method in their toolkit. Others won't care about saving a couple of steps if they get to use the same method every time. This mini-lesson is clear that problem solving strategies are THEIR CHOICE, and that this method is being followed only to demonstrate that it's a method you can ALWAYS use so you should NEVER get "stuck." That's why it's important to have as a problem solving option, and why it's also not important to use it every time (even though the solved problems show you that it CAN be used every time).

The lessons and exercises are typed and the solutions are handwritten on a tablet. Both use some 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.

Please see my three other mini-lessons "Solving One Step Equations", "Cross Multiplication" and "Solving Problems Using Percents" for background skills for this lesson. There is a fourth mini-lesson coming soon, "Percents: Beyond Cross Multiplying" that will demonstrate several other ways to tackle problems involving percents.
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22 including cover page and 8 pages of solutions
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