Math
Grades 6–7 · Pre-Algebra

Order of operations.

PEMDAS is the order math agrees to read an expression in, so everyone gets the same answer. The catch is the part the acronym hides, that multiplication and division are a tie, read left to right. Study Butler makes that nuance click.

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Here is what that looks like.

Study Butler will not print the answer. It points at the next step and lets your kid take it.

An example. The butler answers the question with a question.

is 8 divided by 2 times 4 equal to 1?

careful. multiplication and division do not take turns by rank. they go in reading order. which comes first here.

the division, since it is on the left.

now you see it. work it left to right and try again.

Where students get stuck.

The same few mistakes come up again and again. Here is where the butler slows things down.

01Treating multiplication as always before division

The M before the D in PEMDAS misleads students into a strict ranking. They are actually equal and read left to right. Study Butler corrects this directly, since it causes more wrong answers than almost anything else here.

02Skipping the inside of parentheses

Everything inside parentheses resolves first, including its own internal order. Beginners rush past it. The butler asks what is hiding inside before anything outside gets touched.

03Mishandling negatives and exponents

Whether the negative is inside or outside an exponent changes the answer entirely. Study Butler slows that exact spot down with a careful read of what is being squared.

Bring the problem they're stuck on.

Type it, say it, or snap a photo. Study Butler walks your kid to the answer one question at a time, so they learn it instead of copying it.

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Questions parents ask.

Does multiplication always come before division?
No, and this is the most common misconception. They have equal priority and are performed left to right, just like addition and subtraction. Study Butler makes a point of correcting it early.
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The key is reading the last two pairs as ties, left to right, not as a strict ranking.