The big picture
Fourteen ideas, back in one table.
| Idea | Rule |
|---|---|
| Past one whole | 9/4 and 2 1/4 name the same amount. |
| Making them match | Count up in steps of each bottom number to a shared one. |
| Adding unlike pieces | Rename both, add the tops, keep the bottom. |
| Taking one away | Rename both, subtract the tops, keep the bottom. |
| Wholes and parts | Flatten both, or carry and borrow between wholes and parts. |
| A fraction of a number | Divide by the bottom, multiply by the top. |
| A fraction of a fraction | Multiply the tops, multiply the bottoms. |
| When multiplying shrinks | A top below the bottom shrinks the amount. |
| The flip | Swap top and bottom. The pair multiplies to 1. |
| How many fit | Dividing by a fraction is multiplying by its flip. |
| Cancel first | Before multiplying, divide a top and a bottom by the same number. The answer stays the same. |
| Share a fraction | Multiply the bottom number by the number of shares. The top stays. |
| Which way dividing moves | Dividing by a number between 0 and 1 makes the amount bigger. Dividing by a number above 1 makes it smaller. Dividing by 1 leaves it alone. That holds for any amount above zero. |
| What is left | Find what is left first. Then take the fraction of that, not of the whole. |
Adding and taking away start the same way. Rename both onto one bottom number first. Multiplying needs no shared bottom number.
Your book has Part I, Chapter 8, Working with Fractions. Open it and try its questions.