Memorising by brute force fades. Understanding the patterns behind the tables lasts a lifetime and makes recall faster too. Learn the strategies that rebuild any fact in seconds.
Multiplication tables are not a list to memorise. They are a set of patterns to understand. Learn the patterns, and the facts become obvious rather than forgettable. This guide shows why each fact is true, gives you a rescue strategy for every table, and ends with real problems and a drill so you can test your speed.
Most students are handed a multiplication grid and told to remember it. This works for a while, but the facts fade because they were never attached to meaning. The approach here is the opposite: first the meaning of multiplication, then six strategies that rebuild any fact in seconds. Even if a number slips away under exam pressure, you can always work it out.
Multiplication is a shortcut for adding the same number again and again. 4 × 3 means “four groups of three”, or 3 + 3 + 3 + 3 = 12. Seeing multiplication this way turns an abstract fact into something you can picture, and count if you ever get stuck.
A classroom has 5 tables, each seating 6 students. Instead of counting one by one, 5 × 6 gives the total: 6 + 6 + 6 + 6 + 6 = 30 students.
Two numbers are always involved. They are called factors, and the answer is the product. In 5 × 6 = 30, the factors are 5 and 6 and the product is 30. Two small facts will save you effort straight away: any number times 1 is itself (1 × 9 = 9), and any number times 0 is 0 (0 × 9 = 0).
An array arranges objects into rows and columns. A 4-by-6 array has 4 rows with 6 dots in each row, and counting the dots always gives the same total however you count them. This is what makes multiplication commutative: the order of the factors does not matter.
A muffin tray with 3 rows of 4 muffins holds 12 muffins. Turn the tray sideways and it becomes 4 rows of 3. It is still 12. The picture proves 3 × 4 = 4 × 3 without any calculation.
This one idea cuts your work nearly in half. If 8 × 3 feels hard, flip it to 3 × 8. If the 3-times table is more familiar, use it. The answer, 24, is identical. Here is the exact saving: the 12 × 12 grid has 144 boxes, but only 78 different facts, because each fact appears twice (except the squares like 7 × 7).
Skip counting is the bridge between addition and multiplication. Counting “5, 10, 15, 20…” is the same as reciting the 5-times table one step at a time. Say it aloud, clap it, or jump it along a number line. The rhythm you build is what later recall depends on.
To find 5 × 7, skip count in fives seven times: 5, 10, 15, 20, 25, 30, 35. The seventh number reached is the answer, 35.
Patterns you can use while skip counting: the 2s are all even, the 5s end in 5 or 0, the 10s end in 0, and the 3s have digits that add to a multiple of 3 (for 27, 2 + 7 = 9, which is in the 3 table).
If you know your 2-times table, you already know far more than it seems. Doubling a fact once gives the next table up: double the ×2 fact to get the ×4 fact, and double that to get the ×8 fact.
To find 6 × 8: start with 6 × 2 = 12. Double to get 6 × 4 = 24. Double again to get 6 × 8 = 48.
It is easy to lose count of how many doublings take you from the ×2 fact to the ×8 fact.
The fix: one doubling takes ×2 to ×4 (6 × 4 = 24). You need a second doubling to reach ×8. The chain is 2 → 4 → 8, so double twice starting from the ×2 fact: 12, then 24, then 48. Check: 6 × 8 = 48. ✓
Halving works too. For the 5-times table, remember that 5 is half of 10. To find 5 × 8, work out 10 × 8 = 80 and halve it to get 40.
5 plus one more. For the 6-times table, use the 5-times fact and add one more group: 6 × 7 = 5 × 7 + 7 = 35 + 7 = 42.
The 9-times table has a pattern that makes it one of the easiest to master. For any 9 × n (where n is 1 to 10), the tens digit of the answer is one less than n, and the two digits always add up to 9.
For 9 × 7: one less than 7 is 6, so the tens digit is 6. Since 6 + 3 = 9, the ones digit is 3. The answer is 63. For 9 × 4: tens digit 3, ones digit 6, answer 36.
A physical version: hold up ten fingers and fold down the finger that matches the number you are multiplying by 9. The fingers to the left of the folded one are the tens digit, and the fingers to the right are the ones digit. For 9 × 7, fold down the 7th finger: 6 fingers on the left and 3 on the right, so 63.
One digit slips, and the answer looks believable.
The fix: use the digit-sum check. The digits of every answer in the 9 table add up to 9. For 62, 6 + 2 = 8, which is not 9, so it must be wrong. The correct answer is 63, because 6 + 3 = 9. (This works for 9 × 1 up to 9 × 10.)
The trickiest facts (like 7 × 8 or 6 × 9) can be broken into two easier pieces using the distributive property: split one factor into a sum or a difference, multiply each part separately, then combine.
7 × 8 = (5 × 8) + (2 × 8) = 40 + 16 = 56. Another way: 7 × 8 = 7 × (10 − 2) = (7 × 10) − (7 × 2) = 70 − 14 = 56. Both routes give the same answer, so you can use whichever feels easier.
7 × 8 and 6 × 9 are the two facts people mix up most. Both are in the 50s, and both start with a 5.
The fix: use the memory trick “5, 6, 7, 8”: 56 = 7 × 8. The digits 5, 6 are the answer and 7, 8 are the factors. And 6 × 9 = 54 (digits sum to 9, as in the nines trick). Always check with decomposition: 7 × 8 = 40 + 16 = 56. ✓
Square numbers (a number times itself) are worth knowing by heart: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Different facts respond better to different strategies. Over time, most students settle into two or three favourites, but knowing all of them means there is always a fallback when memory alone is not enough.
| Situation | Best Strategy | Why It Works |
|---|---|---|
| Small numbers, unsure of the pattern | Skip counting | Builds the sequence step by step |
| Visualising a real grouping | Arrays | Shows the total directly, proves commutativity |
| ×4 or ×8 facts | Doubling | Reuses the easier ×2 facts |
| ×5 or ×6 facts | Halving 10s, or 5 plus one more | Builds on the easy ×10 and ×5 facts |
| Any ×9 fact | Nines trick | Digit pattern gives instant answers |
| Table feels unfamiliar (such as ×7) | Commutative flip | Swaps to a more familiar table |
| Large or “stuck” facts (7 × 8, 6 × 9) | Decomposition | Splits into two manageable pieces |
Set aside the tables for 1, 2, 5 and 10, which are easy patterns. Then the facts you really need to work at are those between 3, 4, 6, 7, 8, 9, 11 and 12. Because of the commutative property, that is only 36 different facts, not 144. The doubling, nines and decomposition strategies cover most of them, so the number you must simply memorise is much smaller than it looks.
A baker needs to scale a recipe that makes 6 loaves, but a catering order calls for 8 batches. Rather than adding six repeatedly, the baker uses doubling: 6 × 2 = 12, 12 × 2 = 24, 24 × 2 = 48 loaves for 8 batches. The same doubling strategy used above, applied instantly in a working kitchen.
There are 6 balls in an over. How many balls are bowled in 8 overs? 8 × 6 = 48 balls. (Use doubling: 6 × 2 = 12, 6 × 4 = 24, 6 × 8 = 48.)
A shop sells eggs by the dozen (12). How many eggs are there in 7 dozen? 12 × 7 = 70 + 14 = 84 eggs.
Cloth costs Rs 45 per metre. How much do 8 metres cost? 45 × 8: use decomposition, 40 × 8 = 320 and 5 × 8 = 40, so 320 + 40 = Rs 360.
How many days are there in 52 weeks? 52 × 7 = 50 × 7 + 2 × 7 = 350 + 14 = 364 days. (That is one day short of a normal year.)
Once the tables are secure, you can multiply larger numbers by splitting them into tens and ones. This is the same distributive idea.
(a) 23 × 4 = (20 × 4) + (3 × 4) = 80 + 12 = 92.
(b) 48 × 5: multiply by 10 and halve. 48 × 10 = 480, and half of 480 is 240.
(c) 36 × 25: 25 is a quarter of 100, so 36 × 100 = 3,600 and 3,600 ÷ 4 = 900.
Multiplication facts also give you division facts for free. Since 6 × 7 = 42, you know 42 ÷ 6 = 7 and 42 ÷ 7 = 6. These “fact families” are the foundation for fractions, factors and multiples (see Factors & Multiples).
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1. 2 × 9 = 18, doubled gives 4 × 9 = 36. Nines trick: tens digit is one less than 4, which is 3, and 3 + 6 = 9, so 36. ✓
2. (5 × 7) + (1 × 7) = 35 + 7 = 42. Or (6 × 5) + (6 × 2) = 30 + 12 = 42.
3. 12 × 8 = (10 × 8) + (2 × 8) = 80 + 16 = 96 desks.
1. 8 × 7 = (8 × 5) + (8 × 2) = 40 + 16 = 56.
2. 9 × 6 = 54 pencils.
3. (10 × 6) + (4 × 6) = 60 + 24 = 84.
4. 12 × 7 = 84 runs. Needed to reach 100: 100 − 84 = 16 more runs.
Fluent recall frees a child’s thinking for harder problems later, so tables are worth the effort. But recall is built on understanding, not in spite of it. Use arrays made of counters or buttons, and let children discover that 3 rows of 4 is the same as 4 rows of 3. Teach one strategy at a time, and tie it to a table: doubling for 4s and 8s, the nines trick, and decomposition for the last stubborn facts. Keep practice short, positive and varied. Celebrate the strategy a child used, not just the speed.
A student who only memorises facts has nothing to fall back on when a fact slips their mind under exam pressure. A student who understands these strategies can always rebuild the answer, and over time stops needing to rebuild it at all, because the patterns make the facts stick on their own. Times tables are also the foundation for fractions, percentages, algebra and nearly every topic that follows.
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