Complete number sentences (find the unknown) - Multi-step
Theory
A two-step number sentence is undone in reverse order: undo the last operation first, then the one before it. Check by working forwards.
A two-step sentence uses two operations, such as \(40 + 8 \times \square = 96\).
Undo them in the reverse of the order they were applied.
Here \(40\) was added last, so subtract it first: \(96 - 40 = 56\), then \(56 \div 8 = 7\).
Undo the steps backwards
| Step | Do | Result |
|---|---|---|
| Undo \(+40\) | \(96 - 40\) | \(56\) |
| Undo \(\times 8\) | \(56 \div 8\) | \(7\) |
How to solve a two-step sentence
- Undo the last operation first.
- Undo the first operation next.
- Check by working forwards through the steps.
Subtract the fixed $40, then divide by $8.
\(96 - 40 = 56\), then \(56 \div 8 = 7\).
| \(56 \div 8\) | \(=\) | \(7\) |
\(27 - 6 = 21\), then \(21 \div 3 = 7\).
| \(21 \div 3\) | \(=\) | \(7\) |
\(16 - 4 = 12\), then \(12 \times 2 = 24\).
| \(12 \times 2\) | \(=\) | \(24\) |
\(27 - 3 = 24\), then \(24 \div 6 = 4\).
| \(24 \div 6\) | \(=\) | \(4\) |
Common pitfalls
Frequently asked questions
Why undo in reverse order?
Because the last operation is the outermost one. Removing it first uncovers the step underneath, just like taking off shoes before socks.
How do I start a two-step sentence?
Undo the operation that was applied last. In \(40 + 8 \times \square = 96\), subtract the \(40\) first.
How do I check the answer?
Work forwards through both steps. \(40 + 8 \times 7 = 96\) confirms \(7\).
What does a fixed charge look like?
It is a number added on top of a rate, such as $40 plus $8 an hour, giving \(40 + 8 \times \square\).