Determine a rule from a table of values
Theory
To find the rule in a table, look for what turns every top number into its bottom number, then test it on every row. A rule only counts if it fits them all.
A table of values pairs each top number with a bottom number using one rule.
The rule often multiplies, then adds, such as “\(\times 2\), then \(+3\)”.
Find the multiplier from the step between bottom numbers, then find the amount to add.
Find the rule step by step
| Top | Bottom |
|---|---|
| 1 | \(5\) |
| 2 | \(7\) |
| 3 | \(9\) |
How to find the rule
- Look at the step between bottom numbers to find the multiplier.
- Work out the amount to add so the first row is correct.
- Test the rule on every row.
Rule is \(\times 2\), then \(+3\).
| \(4 \times 2 + 3\) | \(=\) | \(11\) |
Apply the rule to \(20\).
| \(20 \times 2 + 3\) | \(=\) | \(43\) |
Each bottom is \(5\) times the top.
Rule: multiply by \(5\).
| \(3 \times 5\) | \(=\) | \(15\) |
Pay rises by $4 an hour, plus a $5 base.
Rule: \(\times 4\), then \(+5\).
| \(1 \times 4 + 5\) | \(=\) | \(9\) |
Common pitfalls
Frequently asked questions
How do I find a rule from a table?
Find the multiplier from the step between bottom numbers, then find the amount to add so the first row works, and test every row.
Why test more than one row?
Because a rule that fits one row can fail the next. Only a rule that fits every row is correct.
What if the rule is only a multiply?
Then the “add” part is zero. For \(2\to10,\ 3\to15\), the rule is simply multiply by \(5\).
How do I find a far value?
Apply the rule directly. For “\(\times 2\), then \(+3\)”, the top number \(20\) gives \(43\).