Times Tables — Fast Practice & Memory Tricks
The times tables are one of the most useful tools in maths — once you know them by heart, everything gets easier! The good news: you don't need to memorise 100 facts — there are loads of patterns and tricks that do the work for you!
Background and Basic Definitions
The times tables (1 to 10) contain all the multiplication facts. Because multiplication is commutative (\(a \times b = b \times a\)), there are really only 55 different facts (not 100).
Patterns that help you remember:
- Times 1: any number × 1 = that same number. \(7 \times 1 = 7\).
- Times 2: doubling = adding to itself. \(8 \times 2 = 8 + 8 = 16\).
- Times 5: the answer always ends in 0 (even × 5) or 5 (odd × 5). \(7 \times 5 = 35\), \(8 \times 5 = 40\).
- Times 10: add a 0. \(6 \times 10 = 60\).
- Times 9: digit sum rule ← the digits of the answer add up to 9: \(9 \times 7 = 63\), \(6+3=9\). Also: \(9 \times n = 10n - n\).
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
Solution Steps
- Step 1 — Learn the easy rows first: ×1, ×2, ×5, ×10. These 4 rows have simple patterns.
- Step 2 — Practise ×9 with the trick: \(9 \times n = 10n - n\). For example \(9 \times 7 = 70 - 7 = 63\).
- Step 3 — Use commutativity: \(6 \times 8 = 8 \times 6\). If you know 8×6, you don't need to memorise 6×8 separately.
- Step 4 — For trickier facts (×6, ×7, ×8): break them apart — \(7 \times 8 = 7 \times 5 + 7 \times 3 = 35 + 21 = 56\).
- Step 5 — Practise every day with flash cards, games, or timed drills (30 seconds — how many can you get?).
Worked Examples
Example 1: The ×9 Trick
Problem: Calculate \( 9 \times 6 \) using a trick.
Solution:
- Method: \(9 \times 6 = 10 \times 6 - 6 = 60 - 6 = 54\).
- Check using the ×9 digit-sum pattern: \(5 + 4 = 9\). Correct!
Answer: \( 9 \times 6 = 54 \)
Example 2: Breaking into Known Facts
Problem: Calculate \( 7 \times 8 \) by breaking it apart.
Solution:
- \(7 \times 8 = 7 \times (5 + 3) = 7 \times 5 + 7 \times 3\).
- \(7 \times 5 = 35\) (from the ×5 table).
- \(7 \times 3 = 21\) (from the ×3 table).
- \(35 + 21 = 56\).
Answer: \( 7 \times 8 = 56 \)
Example 3: Using Commutativity
Problem: Calculate \( 6 \times 9 \). Is it different from \( 9 \times 6 \)?
Solution:
- \( 9 \times 6 = 54 \) (calculated above).
- \( 6 \times 9 = 9 \times 6 = 54 \) — order does not matter in multiplication.
Answer: \( 6 \times 9 = 54 \)
Example 4: Using a Nearby Fact
Problem: If \( 6 \times 7 = 42 \), what is \( 6 \times 8 \)?
Solution:
- \(6 \times 8 = 6 \times 7 + 6 \times 1 = 42 + 6 = 48\).
- When one factor increases by 1, the product increases by the other factor.
Answer: \( 6 \times 8 = 48 \)
Example 5: Quick Practice — Word Problem
Problem: A box has 8 rows of 7 chocolates. How many chocolates are in the box?
Solution:
- \(8 \times 7 = ?\)
- Break apart: \(8 \times 7 = 8 \times 5 + 8 \times 2 = 40 + 16 = 56\).
Answer: \( 56 \) chocolates.
Common Mistakes
✗ Common mistake: Skipping the "hard" facts (×7, ×8) and trying to work them out every time — takes too long.
✓ The correct way: Memorise the tricky facts by breaking them apart several times until they become automatic. Five minutes a day is enough.
✗ Common mistake: Thinking you need to memorise 100 facts.
✓ The correct way: Because of commutativity and the ×0 and ×1 rows, there are actually only about 36 "hard" facts (×2 through ×9, and only half because of the flip).
✗ Common mistake: For ×9: guessing random answers instead of using the trick.
✓ The correct way: Remember: \(9 \times n = 10n - n\). Or: tens digit = \(n-1\), ones digit = \(10-n\). For \(9 \times 7\): tens = 6, ones = 3, answer = 63.
Practice Tips
- Tip — Learn in this order: ×1, ×2, ×10, ×5, ×9, ×3, ×4, ×6, ×7, ×8. Easiest to hardest.
- Tip — ×9 finger trick: hold up 10 fingers. Fold down finger number n from the left — fingers to the left = tens, fingers to the right = ones. For ×7: fold finger 7, leaving 6 on the left and 3 on the right → 63.
- Tip — ×6 through ×8 are the hardest to remember. Practise just these every day: \(6\times6=36\), \(6\times7=42\), \(6\times8=48\), \(7\times7=49\), \(7\times8=56\), \(8\times8=64\).
- Tip — Song or rhythm: put a fact to a tune. Your brain remembers melodies much better than plain numbers.
Summary and Key Formulas
- ×1: any number — the same number.
- ×2: double (add to itself).
- ×5: ends in 0 or 5.
- ×9: \(9n = 10n - n\), digits add up to 9.
- ×10: add a 0.
- Multiplication is commutative: \(a \times b = b \times a\) — only 55 different facts!
- Tricky facts: break them into known multiplications.