# Slices > Free three-minute lessons on the 20 fraction ideas that trip people up, for kids 8 to 12, the grown-ups helping them, and anyone who never quite got fractions. Slices (https://slices.org): free fraction lessons for children aged 8 to 12, the parents and teachers helping them, and adults who never quite got fractions. Each "slice" is a lesson of about three minutes on one common fraction misunderstanding. The learner makes a prediction, sees what it means in a picture, changes a model to test the idea, answers new questions, and meets the idea again on a later visit. Every lesson works without an account, and progress is saved on the device. A free account (for grown-ups and teenagers 13 and older) keeps progress in sync across devices and adds challenge rounds, mixed practice and the comparison tools in the Fraction Lab. There are no ads and no trackers; the site is funded by donations. Every lesson page also has a complete written explanation. A plain markdown version of each lesson is available by adding ".md" to its URL. ## Slices ### Parts & Wholes Equal shares of a whole, and what each number in a fraction is counting. Start here if fractions feel shaky: every other idea rests on these. - [Equal Means Equal](https://slices.org/slices/equal-means-equal.md): Do the parts of a fraction have to be equal? Why four pieces are not always fourths: a fraction needs equal shares of the whole. - [What’s the Whole?](https://slices.org/slices/whats-the-whole.md): Is half of a large pizza the same amount as half of a small pizza? Why half of a big pizza is more than half of a small one: a fraction depends on its whole. - [The Bottom Number](https://slices.org/slices/the-bottom-number.md): What does the bottom number of a fraction mean? What the bottom number of a fraction counts: all the equal parts that make one whole. - [The Top Number](https://slices.org/slices/the-top-number.md): What does the top number of a fraction mean? What the top number of a fraction counts: how many of the equal parts you have. - [Fractions of Collections](https://slices.org/slices/fractions-of-collections.md): What is 1/4 of 12? How to find a fraction of a group, and why 1/4 of 12 counters is 3, not 1 or 4. ### Fractions Have Size Why 1/8 is smaller than 1/6, why 3/8 is less than 2/3, and how fractions live on the number line, including fractions greater than one. - [The Bigger Denominator Trap](https://slices.org/slices/bigger-denominator-trap.md): Is 1/6 bigger than 1/8? Why 1/8 is smaller than 1/6, even though 8 is bigger than 6. - [The Bigger Numerator Trap](https://slices.org/slices/bigger-numerator-trap.md): Which is bigger, 3/8 or 2/3? Why 2/3 is bigger than 3/8, even though 3 is bigger than 2. - [More Than One Whole](https://slices.org/slices/more-than-one-whole.md): Can a fraction be bigger than 1? Why 6/4 makes sense: a fraction can equal one whole or go beyond it. - [Counting Spaces, Not Ticks](https://slices.org/slices/counting-spaces-not-ticks.md): How do you find 3/4 on a number line? Why we count equal spaces from 0, not tick marks, to find 3/4 on a number line. - [One Number, Not Two](https://slices.org/slices/one-number-not-two.md): Where is 2/5 on a number line? Why 2/5 is one number between 0 and 1, not a 2 and a 5. ### Same Value, Different Forms How 1/2 and 2/4 can be the same number, why simplifying never shrinks a fraction, and how to compare fractions by reasoning instead of guessing. - [Different Numbers, Same Amount](https://slices.org/slices/different-numbers-same-amount.md): Is 1/2 the same as 2/4? Why 1/2, 2/4 and 4/8 are exactly the same amount, even though the numbers are different. - [Simplifying Doesn’t Shrink](https://slices.org/slices/simplifying-doesnt-shrink.md): Does simplifying a fraction make it smaller? Why 6/8 and 3/4 are the same amount, and why simplifying a fraction never makes it smaller. - [Same Bottom, Compare the Top](https://slices.org/slices/same-bottom-compare-the-top.md): How do you compare fractions with the same denominator? Why 5/7 is bigger than 2/7: the pieces are the same size, so the one with more pieces is bigger. - [Same Top, Compare the Pieces](https://slices.org/slices/same-top-compare-the-pieces.md): How do you compare fractions with the same numerator? Why 3/5 is bigger than 3/8: the same number of pieces, but fifths are bigger pieces than eighths. - [Compare Without Guessing](https://slices.org/slices/compare-without-guessing.md): Which is bigger, 3/8 or 4/7? How to compare fractions like 3/8 and 4/7 by asking which side of one half each one is on. ### Working With Fractions Why we need common units to add and subtract, why multiplying can make a number smaller, and why dividing can make it bigger. - [Adding Different Pieces](https://slices.org/slices/adding-different-pieces.md): Is 1/2 + 1/4 equal to 2/6? Why 1/2 + 1/4 is 3/4, not 2/6: make the pieces the same size before you count them. - [Keep the Unit When Adding](https://slices.org/slices/keep-the-unit-when-adding.md): Is 1/5 + 2/5 equal to 3/10? Why 1/5 + 2/5 is 3/5, not 3/10: joining fifths gives more fifths, not smaller pieces. - [Taking Pieces Away](https://slices.org/slices/taking-pieces-away.md): Is 3/4 − 1/2 equal to 2/2? Why 3/4 − 1/2 is 1/4, not 2/2: take away an amount using same-size pieces. - [Multiplication Can Make Smaller](https://slices.org/slices/multiplication-can-make-smaller.md): Why does multiplying by a fraction make a number smaller? Why 1/2 × 1/2 is 1/4: multiplying by a fraction less than one takes part of an amount. - [Division Can Make Bigger](https://slices.org/slices/division-can-make-bigger.md): Why does dividing by a fraction give a bigger answer? Why 1/2 ÷ 1/4 is 2: dividing by a fraction asks how many of those pieces fit. ## Guides - [Find my first slice](https://slices.org/start): an adaptive check of up to eight questions that suggests where to start. - [All slices](https://slices.org/explore): the 20 lessons, organized into four families. - [The Fraction Lab](https://slices.org/lab): build a fraction and see it as a bar and a point on the number line; account holders can compare two fractions in same-size pieces. - [For parents](https://slices.org/parents): how to help with fractions at home, and what to say. - [For teachers](https://slices.org/teachers): classroom use, diagnostic questions and Common Core alignment. - [Glossary](https://slices.org/glossary): fraction words explained in plain language. ## Optional - [Full text of every slice](https://slices.org/llms-full.txt) - [Machine-readable catalog (JSON)](https://slices.org/slices.json) - [Why we made Slices, and the research behind it](https://slices.org/about) - [Support Slices with a donation](https://slices.org/donate)