The big picture
A chit like 3 × 25 + 40 has a value. Twelve ideas tell you how to find it.
| Idea | What it means |
|---|---|
| Expression and value | An expression is written out. Its value is a number. |
| Order changes it | Same line, two orders, two answers. So we agree one. |
| Terms | Work out each term. Then add the terms. |
| Brackets | Finish inside the brackets first. |
| Tied signs | Same level? The left one goes first. |
| Turning round | + and × swap. − and ÷ usually change the value. |
| One tray, two counts | 6 × (10 + 3) equals 6 × 10 + 6 × 3. |
| Write your own | One term per item, then check the size. |
| Swap and regroup | Swap two terms. The total stays the same. Group the terms a different way. The total stays the same. |
| Brackets away | A minus before a bracket flips every sign inside. A plus before a bracket changes no sign. |
| Compare by moves | A sum stays equal when one term gains what the other loses. A difference stays equal when both terms move by the same amount. |
| Near 100 | Write the number as 100 plus or minus a small gap. Multiply each part by the other number. Then subtract the gap's part, or add it. |
A line of numbers and signs is a set of steps. Anyone can do the steps and reach the same value.