The chart
Find one number in the top row and the other in the left column. The product is where the row and the column meet. The chart is symmetric: the row for 7 reads the same as the column for 7.
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
The grid has 144 cells, but because a × b equals b × a, only 78 of them are different products. Five tables, the 1s, 2s, 5s, 10s and 11s, follow patterns so simple that nobody memorizes them. Take those out, and the products of the remaining 7 numbers (3, 4, 6, 7, 8, 9, 12) with each other are what is left: 28 facts.
The tables with a pattern
1s and 10s. One times a number is the number. Ten times a number is the number with a 0 on the end: 10 × 7 = 70, 10 × 12 = 120. These two rows also anchor the rest: the percentage calculator is built on the same idea, since 10 percent of a number is the number with the last digit moved past the decimal point.
2s. Two times a number is the number doubled, and every answer is even: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. The last digit cycles through 2, 4, 6, 8, 0.
5s. Every answer ends in 0 or 5: an even number times 5 ends in 0, an odd number times 5 ends in 5. The quickest way to get the product is to take ten times the number and halve it.
| 5 × n | 10 × n | Half of that |
|---|---|---|
| 5 × 3 | 30 | 15 |
| 5 × 7 | 70 | 35 |
| 5 × 9 | 90 | 45 |
| 5 × 12 | 120 | 60 |
11s. Up to 9, the product is the digit written twice: 11 × 1 = 11, 11 × 2 = 22, 11 × 3 = 33, 11 × 4 = 44, 11 × 5 = 55, 11 × 6 = 66, 11 × 7 = 77, 11 × 8 = 88, 11 × 9 = 99. For 11 × 10, 11 × 11 and 11 × 12 the carry breaks the pattern: 110, 121, 132.
4s. Four times a number is the number doubled, then doubled again. That turns the 4s into two steps of the 2s.
| 4 × n | Double once | Double again |
|---|---|---|
| 4 × 3 | 6 | 12 |
| 4 × 6 | 12 | 24 |
| 4 × 7 | 14 | 28 |
| 4 × 9 | 18 | 36 |
| 4 × 12 | 24 | 48 |
6s. When the number is even, six times it ends in the same digit as the number: 6 × 2 = 12, 6 × 4 = 24, 6 × 8 = 48. For the odd numbers there is no such shortcut, but 6 × n is 5 × n plus n, so 6 × 7 is 35 + 7 = 42.
| 6 × even | Product | Last digit |
|---|---|---|
| 6 × 2 | 12 | 2 |
| 6 × 4 | 24 | 4 |
| 6 × 6 | 36 | 6 |
| 6 × 8 | 48 | 8 |
| 6 × 12 | 72 | 2 |
9s. Two patterns at once. The tens digit is one less than the number, and the two digits add up to 9, so 9 × 7 has a 6 in the tens place and 9 − 6 = 3 in the ones place: 63. The finger trick in the FAQ is the same pattern on your hands.
| 9 × n | Product | Tens | Ones | Digit sum |
|---|---|---|---|---|
| 9 × 1 | 9 | 0 | 9 | 9 |
| 9 × 2 | 18 | 1 | 8 | 9 |
| 9 × 3 | 27 | 2 | 7 | 9 |
| 9 × 4 | 36 | 3 | 6 | 9 |
| 9 × 5 | 45 | 4 | 5 | 9 |
| 9 × 6 | 54 | 5 | 4 | 9 |
| 9 × 7 | 63 | 6 | 3 | 9 |
| 9 × 8 | 72 | 7 | 2 | 9 |
| 9 × 9 | 81 | 8 | 1 | 9 |
| 9 × 10 | 90 | 9 | 0 | 9 |
The digit sum of every multiple of 9 is 9 or a multiple of 9, so you can check an answer in a second: 9 × 12 = 108, and 1 + 0 + 8 = 9. The same test is how you tell whether a bigger number divides by 9 at all, which is what the prime factorization calculator works out for any number.
The tables without one: 3, 7, 8 and 12
These are built from tables you already know rather than from a pattern of their own.
- 3s. Double the number and add the number once more: 3 × 8 = 16 + 8 = 24. The digit sum of every multiple of 3 is divisible by 3, the same check as for 9.
- 8s. Double three times: 8 × 7 is 14, 28, 56. Or take the 4s and double once.
- 12s. Ten times the number plus two times the number: 12 × 7 = 70 + 14 = 84. This is the same split a long multiplication makes on paper.
- 7s. The only table with no shortcut, because 7 is prime and not next to 10 or 5. Five times the number plus two times the number works: 7 × 8 = 40 + 16 = 56. Most of the 7s are also covered from the other side, since 7 × 4 is in the 4s and 7 × 9 is in the 9s.
The facts that are commonly the hardest
Ask around and the same products come up: both factors from the tables without a pattern, and nothing in the answer to hold on to. They are commonly reported as the facts people get wrong longest, which is a reason to give them more practice than the rest, not a reason to worry.
| Fact | Answer | Way in |
|---|---|---|
| 6 × 7 | 42 | 30 + 12 |
| 6 × 8 | 48 | 30 + 18 |
| 7 × 8 | 56 | 35 + 21 |
| 6 × 9 | 54 | digit sum: 5 + 4 = 9 |
| 7 × 9 | 63 | digit sum: 6 + 3 = 9 |
| 8 × 9 | 72 | digit sum: 7 + 2 = 9 |
| 7 × 12 | 84 | 70 + 14 |
| 8 × 12 | 96 | 80 + 16 |
| 9 × 12 | 108 | 90 + 18 |
A few have a hook of their own. 7 × 8 = 56 reads 5, 6, 7, 8 when you write the answer first. 6 × 6 = 36 and 12 × 12 = 144 are squares, which tend to stick because they are said so often. 6 × 8 = 48 is 6 × 4 doubled.
The tables backwards
Every multiplication fact is also two division facts: 7 × 8 = 56 means 56 ÷ 7 = 8 and 56 ÷ 8 = 7. Division is where the tables earn their keep, from sharing a bill to every step of a long division, where you ask how many times the divisor fits and the answer comes straight from the table. The long division calculator shows those steps one by one, which makes a good check after working a problem on paper. The tables also decide common multiples and common factors: 24 is in the 6s and the 8s, so it is a common multiple of 6 and 8, and the LCM and GCF calculator finds the least one for any pair.
A practice routine
- Learn the tables in this order: 2, 10, 5, 11, 4, 3, 6, 9, 8, 7, 12. Each new table reuses an earlier one, and the tables without a pattern come last, when most of their facts are already known from the other direction.
- One new table at a time, said out loud in order, then out of order. Move on when every fact comes in under about three seconds.
- Mix in the old tables. Each session, ask a handful of facts from every table already learned, so nothing fades while the next one is being added.
- Ask both directions. For every 6 × 7, also ask 42 ÷ 6 and 42 ÷ 7, and ask the mirror, 7 × 6.
- Give the hard list extra turns. The 9 facts in the table above deserve a card each. When one is wrong, say the whole fact out loud and ask it again two minutes later.
- Keep sessions short. A few minutes every day beats one long sitting, and the chart on this page is there to check an answer rather than to look one up.
Frequently asked questions
Which times tables should a child learn first?
The 2s, 10s and 5s, because each has a pattern you can hear and see: doubling, adding a zero, ending in 0 or 5. Then the 11s and the 4s, which are the 2s doubled. The 3s, 6s, 9s, 8s, 7s and 12s come last, with 9 made easy by the digit-sum pattern.
Do I really need to memorize all 144 facts?
No. Because 7 × 8 and 8 × 7 are the same fact, the 12 by 12 grid holds only 78 different products. Take out the 1s, 2s, 5s, 10s and 11s, which follow simple patterns, and 28 facts are left to memorize outright. Most of the effort goes into those.
What is the 9 times table finger trick?
Hold up both hands, palms facing you, and number the fingers 1 to 10 from the left. To multiply 9 by a number, fold down that finger. The fingers to the left of it are the tens digit and the fingers to the right are the ones digit. For 9 × 4, fold the fourth finger: 3 fingers left, 6 right, so 36.
Why does the 11 times table stop repeating the digit at 10?
Up to 9 × 11 the product is the digit written twice, because 11 × k is 10k + k and both digits stay below 10. From 10 × 11 the tens column carries over, so 11 × 11 is 121 and 12 × 11 is 132. A second pattern works there: add the two digits of the number and put the sum in the middle, so 1 and 2 with 3 between them gives 132.
How long does it take to learn the times tables?
It depends on how often you practice, not how long each session is. Five minutes a day on one table, mixed in with questions from tables already known, works better than one long session a week. Practice the facts in both directions, 7 × 8 = 56 and 56 ÷ 7 = 8, because division is where the tables are used most later on.