Addition and Subtraction: More Bad Behavior by Dear Aunt Sally

Attention:  Dear Aunt Sally may not be fit for teaching students algebra!

A problem has been discovered in sweet Aunt Sally’s little memory trick:  Please Excuse My Dear Aunt Sally.

Actually, make that two problems.

The first, revealed in my 9/9 post below, is that Aunt Sally wrongly makes students think they’re supposed to multiply before dividing. That’s because the word My (standing for MULTIPLY) comes before Dear (standing for DIVIDE).

Countless students have been deceived into thinking they’re supposed to multiply before dividing [See the 9/9 post for the full run-down on this problem.]

Today I want to point out another problem, and offer two solutions.

The second problem is that, since “Aunt” (standing for ADD) comes before “Sally” (standing for SUBTRACT), countless other students have been led to think they are supposed to ADD before they SUBTRACT.

Well, what are students supposed to do?

First of all, students need to realize that adding and subtracting are at exactly the same level of hierarchy as each other. But if that’s true, how can students ever decide which to do first.

Easy! Same solution as with multiplying and dividing. We simply look to see which of these  operations is written first as we read the problem left to right.

Example:  in the expression  8 + 3 – 4, the addition symbol precedes the subtraction symbol, so here we add before subtracting. And we simplify the expression like this:

8 + 3 – 4
=  11 – 4
= 7

But in the expression   8 – 3 + 4
the subtraction symbol is written before the addition symbol, so here we subtract before we add, and we simplify the expression like this:

8 – 3 + 4
=  5 + 4
=  9

It’s really that simple. Pay attention to which operation sign comes first as you read the problem from left to right. Then do the operations in the correct order based on that.

One other solution:  in my book, the Algebra Survival Guide, I get away from the Please Excuse My Dear Aunt Sally approach, as I create my own memory trick, one that involves Strawberry Mousse. If you want to take a look at this approach, check out my book at this site.

From the homepage, click the link that says:  View Sample Chapters of the Algebra Survival Guide, and download the chapter on Positive and Negative

Cover of

Cover via Amazon


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