Division is repeated subtraction

Multiplication is repeated addition. My math methodologies teacher taught us how to show students that multiplication is a short-cut for adding the same thing over and over. The curriculum I’m currently teaching has an entire lesson devoted to teaching children that multiplication is a short-cut for repetitive addition problems.

Logically, it follows that division is repeated subtraction. It’s a short-cut for subtracting the same thing over and over.

So why do so many students resort to addition to solve a division problem? Is it because we don’t help them make that connection, or do they just fall back to what’s familiar?

Translating percent problems into solvable equations

It’s usually pretty easy to see when you have a percent problem on your hands. They generally come in one of three varieties:

• x is what percent of y?
• What is z percent of y?
• x is what percent of z?

When you understand how x, y, and z fit together, solving percent problems becomes a snap. I’m going to show you two different ways to tackle each type of question, one using proportions, and one using a straightforward equation. Both work, so pick the one that makes more sense for you.

1. x is what percent of y?

=     OR    x = ? * y

2. What is z percent of y?

=     OR    ? = z * y

3. x is z percent of what?

=     OR    x = z * ?

It’s really just two simple formulas that can be adapted to whichever situation you’re in. Just insert the numbers you know, and solve for the one you’re missing. Beware, though. If you choose the multiplication formula, make sure to convert the percent into a decimal!

Why do I have to learn algebra?

Because there’s more to algebra than just the math.

Algebra is really about learning how to apply math to real world situations. It’s about setting up the right equation to give you the answer you need when you need it. It’s about modeling data to help you make good decisions. It’s about making sure you’re getting a fair deal.

In short, algebra teaches you to think critically. It teaches you to look at what you have, and to use what you have efficiently to find what you need. It teaches you to look at patterns, translate them, and apply them. It teaches you to make connections, to apply what you learned in one situation to a seemingly random situation.

It also lays the groundwork for you to be successful in geometry and any later math classes you choose to take, thereby allowing you to graduate and move on to successfully complete your math requirements in college. And those critical thinking skills come in handy regardless of your discipline. Being able to extract the right information and work with it will get you pretty far through your career.

So, the next time you complain about how you’re never going to use what you’re learning in algebra class, remember that even if you don’t use everything, you are still coming away with valuable life skills.