Want to learn the 31 times table faster? There is a simple pattern that helps you calculate 31 × 1 through 31 × 9 quickly. Instead of memorizing every answer separately, use the relationship between 31, 30, and 1.
This visual math trick is useful for students, parents, teachers, and anyone who wants to build faster mental-math skills. The main idea is simple: multiply by 30, multiply by 1, and add the two results together.
The Easy 31 Multiplication Trick
Why does this work? Because 31 is made of 30 + 1:
So when you multiply 31 by any number n, you can distribute the multiplication:
For example, when n = 7:
The 31 Times Table Pattern
For single-digit multipliers from 1 through 9, the answer can be viewed as two parts: the result of 3 × n followed by n. A leading zero is added when needed so that the place values stay clear.
For example:
This is why the answers in the video have a repeating visual structure:
- 31 × 1 = 031, which is 31 when the leading zero is removed.
- 31 × 2 = 062, which is 62 when the leading zero is removed.
- 31 × 3 = 093, which is 93 when the leading zero is removed.
- 31 × 4 = 124.
- 31 × 9 = 279.
31 × 1 Through 31 × 10
Here is the complete table. The first nine rows show the visual pattern most clearly. The final row shows the standard result for multiplying by 10.
| Multiplication | Pattern View | Answer |
|---|---|---|
| 31 × 1 | 03 | 1 | 31 |
| 31 × 2 | 06 | 2 | 62 |
| 31 × 3 | 09 | 3 | 93 |
| 31 × 4 | 12 | 4 | 124 |
| 31 × 5 | 15 | 5 | 155 |
| 31 × 6 | 18 | 6 | 186 |
| 31 × 7 | 21 | 7 | 217 |
| 31 × 8 | 24 | 8 | 248 |
| 31 × 9 | 27 | 9 | 279 |
| 31 × 10 | 31 × 10 | 310 |
How to Use the Trick in Your Head
Example 1: 31 × 6
Multiply 30 × 6 to get 180, then add 6:
Example 2: 31 × 9
Multiply 30 × 9 to get 270, then add 9:
Example 3: 31 × 10
When multiplying by 10, simply move the digits one place to the left and add a zero:
Why the Pattern Works
The pattern is based on place value and the distributive property:
Since 30n = 10 × 3n, the answer can also be written as:
For single-digit n values from 1 through 9, this creates the visual “3n followed by n” pattern. It is not a new multiplication rule; it is a faster way to see the ordinary place-value calculation.
Common Mistakes to Avoid
Do not apply the visual pattern carelessly to every multiplier. It is most useful for the single-digit multipliers 1 through 9. For 31 × 10, the answer is 310, not 3010. Use the regular ×10 rule for that calculation.
Also remember the leading zeros in the first three pattern rows. The pattern view 03 | 1 represents 031, which is simply 31. Likewise, 06 | 2 represents 062, which equals 62.
Finally, do not confuse 31 × n with 3 × n. The first part of the visual pattern comes from 30 × n, while the final digit comes from 1 × n.
Practice Problems
Try solving these without a calculator:
- 31 × 2
- 31 × 5
- 31 × 7
- 31 × 9
- 31 × 10
Answer Key
- 31 × 2 = 62
- 31 × 5 = 155
- 31 × 7 = 217
- 31 × 9 = 279
- 31 × 10 = 310
Final Takeaway
To calculate 31 × n quickly, remember that 31 is 30 + 1:
For single-digit multipliers, this creates the memorable pattern shown in the video: calculate 3 × n, place n after it, and keep the place values correct. This makes the 31 times table easier to learn and helps build confidence with mental multiplication.
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