Lesson 2.1 — Dividing Fractions by Fractions

Hey there! Today we're dividing fractions, and I promise it's friendlier than it sounds.

Here's the big idea. Division really just asks one question: how many of these fit into that? So when you see three divided by one half, you're really asking, how many halves are there in three? Picture three whole pizzas, and you slice each one in half. That gives you six half-pieces. So three divided by one half equals six.

Now, you won't always want to draw pizzas, so here's the shortcut every mathematician uses. It's called keep, change, flip. Keep the first fraction exactly as it is. Change the divide sign into a multiply sign. And flip the second fraction upside down. That flipped fraction has a fancy name: the reciprocal. Three fourths flipped becomes four thirds. The number five flipped becomes one fifth.

Let's try one. How many eighths fit in three fourths? We write three fourths divided by one eighth. Keep three fourths. Change divide to multiply. Flip one eighth to eight over one. Now multiply across: three fourths times eight is twenty-four over four, which is six. Six eighth-pieces fit perfectly inside three fourths.

One thing that surprises a lot of students: dividing made the answer bigger! That's totally normal. When you divide by a number smaller than one, lots of little pieces fit inside, so the result grows.

Quick recap. Dividing by a fraction means how many fit. Use keep, change, flip: keep the first, change the sign, flip the second to its reciprocal, then multiply. That's it. You've got this!