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A hall needed 200 chairs. Two people counted them two different ways.

Your book's chapter is We Distribute, Yet Things Multiply. That is Part I, Chapter 6. It is about one rule: the distributive property. To distribute is to share out. Here a multiplication is shared out over a sum. A sum is made of terms. In 20 + 5, the terms are 20 and 5.

What you will learn

• The cut that moves nothing — a block's two parts add up.
• Open a bracket — the outside number meets every term inside.
• A letter inside — the same move, even with no value yet.
• A minus inside — each term keeps its own sign.
• Two brackets — every term in one meets every term in the other.
• Joining terms — only matching parts may gather.
• A squared sum — a sum times itself. Its middle piece is easy to forget.
• Splitting on purpose — cut a number where it helps you.

Every idea has a lab. Tap or slide, and watch the bracket open.