How to add and subtract fractions.

Adding fractions trips kids up because the rule feels arbitrary: why can you add the tops but not the bottoms? Study Butler starts with what a denominator actually is, so the common-denominator step makes sense instead of feeling like a trick.

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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.

what is one half plus one third.

you cannot add them yet. the pieces are different sizes. what size could both halves and thirds turn into.

sixths?

good. rewrite both as sixths and then the tops are safe to add.

Where students get stuck.

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

01Adding the denominators

Students add straight across, top and bottom, turning one half plus one third into two fifths. Study Butler asks what the bottom number actually means, which is exactly why you cannot just add it.

02Forgetting to find a common denominator

You can only add fractions once the pieces are the same size. The butler always has your kid confirm the denominators match before touching the tops.

03Not simplifying the answer

An answer like four eighths is correct but not finished. Study Butler asks whether the fraction can be written in smaller numbers, which builds the habit of simplifying.

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.

Why do fractions need a common denominator to add?

Because you can only add pieces that are the same size. Halves and thirds are different-sized pieces, so you rewrite both as a shared size first. Study Butler grounds the rule in that idea rather than asking your kid to memorize it.

How do you find the lowest common denominator?

Find the smallest number both denominators divide into evenly. Study Butler walks your kid through listing multiples until one lines up, so the method makes sense.

Keep going.

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