Why is learning times tables important?

Times tables underpin almost every area of mathematics: long multiplication and division, fractions, percentages, ratio, algebra, and geometry all rely on instant recall of multiplication facts. Students who have fluent times tables tackle higher mathematics faster and with greater confidence.

What is the commutative property of multiplication?

The commutative property states that a × b = b × a for all numbers a and b. In practice, this means you only need to memorise half the facts in a 12×12 chart — once you know 7 × 8 = 56, you automatically know 8 × 7 = 56. This reduces 144 facts to 78 unique facts.

Updated April 15, 2026 Full 1–12 Chart Practice Quiz Speed Test

Math Times Tables

Q: What are math times tables?

Math times tables, also called multiplication tables or maths times, are organised charts or lists showing the results of multiplying one number by another. A standard times tables chart covers the facts from 1×1 to 12×12, producing 144 multiplication facts that form the foundation of arithmetic.

Q: Which times tables should I learn first?

Learn tables in this order: start with 1, 2, 5, and 10 (strong patterns make these easiest), then learn 3, 4, 6, and 9 (moderate difficulty), and finish with 7, 8, 11, and 12 (hardest). This sequencing builds momentum and confidence.

Q: How long does it take to memorise all times tables?

With daily 10–15 minute practice sessions, most students achieve full fluency across all 12 times tables in 6–12 weeks. Consistency matters more than session length. Short daily practice outperforms infrequent long sessions.

Q: What is the quickest trick for the 9 times table?

Hold all ten fingers out. To calculate 9 × n, fold down finger number n from the left. The fingers to the left of the folded finger give the tens digit; the fingers to the right give the units digit. For example, 9 × 7: fold down finger 7. You have 6 fingers left and 3 fingers right, giving 63.

Q: How do I help my child learn times tables at home?

Display a times table chart where your child studies. Practise together for 10 minutes daily. Use the interactive modes on He Loves Math — quiz mode for guided learning, speed test for challenge. Test them randomly throughout the day on facts they have just learned. Celebrate correct answers and progress milestones.

Q: Are there patterns I can use to learn times tables faster?

Yes. The 2s are all even. The 5s end in 0 or 5. The 10s just add a zero. The 9s produce digit pairs that sum to 9 (18, 27, 36…). The 11s repeat the digit up to 9 (11×3=33). The 4s are double the 2s, and the 8s are double the 4s. Using these patterns cuts memorisation in half.

Your complete interactive resource for mastering math times tables from 1 to 12. View the full multiplication chart, practise with a randomised quiz, study individual tables, or challenge yourself with a 20-question speed test — all in one place, completely free.

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Open the tool Why times tables matter

Quick Answer: The Multiplication Formula

Every fact in a times table is an application of the definition of multiplication as repeated addition:

$$a \times b = \underbrace{a + a + a + \cdots + a}_{b \text{ times}}$$

The commutative property means order does not matter:

$$a \times b = b \times a$$

This single property halves the number of unique facts in a 12×12 chart — from 144 down to just 78. Know one, and you automatically know its pair.

Interactive Math Times Tables Tool

Choose a mode below. Complete Chart shows the full grid. Practice Quiz tests selected tables with instant feedback. Individual Tables lists any single table. Speed Test challenges you to answer 20 questions as fast as possible.

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Complete Chart

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Practice Quiz

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Individual Tables

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Speed Test

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What Are Math Times Tables?

Math times tables — also called multiplication tables or maths times — are organised lists or grids showing the products of multiplying a given number by a series of whole numbers, typically 1 through 12. The standard 12×12 times table grid contains 144 cells, each holding the product of a row number and a column number. These 144 facts are the pre-computed answers to every multiplication involving numbers from 1 to 12.

The concept dates at least to ancient Babylon (around 1800 BCE), where clay tablets show multiplication tables used for commerce, taxation, and astronomy. The particular format of a 12×12 grid became standard in England and much of Europe during the medieval period, partly because of the traditional importance of the number 12 in weights, measures, and currency (12 pence to a shilling, 12 inches to a foot, 12 months in a year).

Today, times tables remain the foundational calculation tool taught in primary schools worldwide. They are not merely arithmetic facts to memorise — they are the cognitive infrastructure on which all higher mathematics is built, from fractions and percentages to algebra, calculus, and statistics.

Key insight: Because of the commutative property $ a \times b = b \times a $, a 12×12 grid contains only 78 unique facts (66 non-square pairs plus 12 square numbers). If you know 7 × 9 = 63, you already know 9 × 7 = 63. This insight alone cuts the memorisation workload nearly in half.

The Mathematics Behind Times Tables

Understanding the mathematical properties that govern times tables makes memorisation both faster and more resilient. Rather than learning isolated facts, you learn a connected web of relationships. Here are the four most important mathematical properties at work in every times table.

1. Multiplication as Repeated Addition

Definition of Multiplication $$a \times b = \underbrace{a + a + a + \cdots + a}_{b \text{ times}} \quad \text{for positive integers } a, b$$

So $ 7 \times 4 = 7 + 7 + 7 + 7 = 28 $. This definition makes the tables learnable by skip-counting — a skill most children already know.

2. Commutativity

Commutative Property $$a \times b = b \times a \quad \text{for all integers } a, b$$

The 12×12 grid is symmetric along its main diagonal. Every fact above the diagonal has a mirror below it. Memorising one cell gives you two facts for free.

3. Distributive Property (The Key to Tricks)

Distributive Law $$a \times (b + c) = a \times b + a \times c$$

This property is the mathematical basis for every "split the number" trick. For example, to calculate $ 7 \times 13 $, split 13 = 10 + 3:

$$7 \times 13 = 7 \times 10 + 7 \times 3 = 70 + 21 = 91$$

This is also why the 4 times table is just double the 2 times table, and the 8 times table is double the 4 times table — because $ 4 \times n = 2 \times 2 \times n $ and $ 8 \times n = 2 \times 4 \times n $.

4. Square Numbers

Square Numbers $$n^2 = n \times n \quad (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144)$$

The 12 square numbers on the main diagonal of the chart are anchor facts — memorise these first, and all off-diagonal facts become easier to estimate by proximity.

Patterns in Every Times Table

Every times table has at least one recognisable pattern. Learning to see these patterns transforms multiplication from rote memorisation into pattern recognition — a much more durable skill.

× 1 — Identity

Any number times 1 equals itself: $ n \times 1 = n $. Nothing changes.

× 2 — All Even

Every product is even. The sequence is the counting numbers doubled: 2, 4, 6, 8, 10…

× 3 — Digit Sum

The digits of each product sum to a multiple of 3: 12 (1+2=3), 27 (2+7=9), 36 (3+6=9).

× 4 — Double of 2s

The 4 times table is exactly double the 2 times table. $ 4 \times n = 2 \times (2 \times n) $.

× 5 — Ends in 0 or 5

All products end in either 0 or 5, alternating: 5, 10, 15, 20, 25, 30…

× 6 — Even + Same

When 6 is multiplied by an even number, the units digit matches the multiplier: $ 6 \times 4 = 24 $.

× 9 — Digit Sum = 9

The digits of every product from 9×1 to 9×10 sum to 9: 18 (1+8), 27 (2+7), 36 (3+6)…

× 10 — Add Zero

Multiply any number by 10 by writing a zero after it: $ 10 \times n = n0 $.

× 11 — Double Digit

For single digits, the answer repeats the digit: $ 11 \times 3 = 33 $, $ 11 \times 7 = 77 $. For 11 × 11 and 11 × 12, use the distributive law.

× 12 — Tens + Twos

Split: $ 12 \times n = 10 \times n + 2 \times n $. So $ 12 \times 7 = 70 + 14 = 84 $.

Which Times Table Should You Learn First?

Not all times tables are equally difficult. Learning them in a thoughtful sequence means each new table feels manageable because it builds on what you already know.

Stage	Tables	Why These First	Key Pattern
Stage 1 (Easiest)	× 1, × 2, × 5, × 10	Clear rules, strong patterns, often already known	Even numbers / ends 0 or 5 / add zero
Stage 2 (Medium)	× 3, × 4, × 6, × 9	Digit sum rules and doubling strategies help greatly	Digit sums / double of 2s / 9s trick
Stage 3 (Hardest)	× 7, × 8, × 11, × 12	Fewer shortcuts; rely on distributive law and anchor facts	7 × 8 = 56; 8s double 4s; 12n = 10n + 2n

By the time a learner reaches Stage 3, they already know the commutative pairs of many hard facts from Stage 1 and 2. For example, $ 7 \times 3 $ is already known when they mastered the 3 times table in Stage 2 — so they only need to learn $ 7 \times 7 = 49 $ and the pairs involving 8, 11, and 12 as genuinely new facts.

Quick Tricks and Mental Shortcuts

The 9s Finger Trick

Hold all ten fingers in front of you. To calculate $ 9 \times n $: fold down finger number n from the left. Count the fingers to the left of the folded finger — this is the tens digit. Count the fingers to the right — this is the units digit.

$$9 \times 7: \text{ fold finger 7} \Rightarrow \underbrace{6}_{\text{left}} \text{ fingers} \mid \underbrace{3}_{\text{right}} \text{ fingers} = \boxed{63}$$

Doubling Strategy for 4s and 8s

$$4 \times n = 2 \times (2 \times n) \qquad 8 \times n = 2 \times (2 \times (2 \times n))$$

Example: $ 8 \times 7 $. Double 7 = 14. Double 14 = 28. Double 28 = 56. So $ 8 \times 7 = 56 $.

The Distributive Split for 7s and 12s

$$7 \times n = (5 \times n) + (2 \times n) \qquad 12 \times n = (10 \times n) + (2 \times n)$$

Example: $ 7 \times 8 = (5 \times 8) + (2 \times 8) = 40 + 16 = 56 $.

Proven Learning Strategies

Research in cognitive psychology consistently supports certain learning methods over others for building automaticity — the ability to recall facts instantly without conscious calculation.

Spaced repetition. Practice facts at increasing intervals rather than all at once. Review a new table daily for a week, then every few days, then weekly. Spacing prevents rapid forgetting and builds long-term retention.
Interleaved practice. After learning table A and table B separately, practice them together in random order. This forces your brain to distinguish between facts and strengthens retrieval pathways more than blocked practice.
Retrieval practice (quiz yourself). Attempting to recall a fact from memory — rather than re-reading it — is the single most effective study technique. Use the Practice Quiz mode above to implement this immediately.
Immediate corrective feedback. When you answer incorrectly, see the right answer immediately and repeat it. Delayed feedback dramatically reduces the learning value of each practice session.
Build automaticity with speed tests. Once you can answer correctly at your own pace, begin timed practice. Automaticity — not just accuracy — is the goal, because it frees mental resources for higher-order thinking during multi-step problems.

Complete Times Tables 1 to 12 — Reference Lists

The lists below show every fact for each table up to × 12. Use these for reference, printable practice, or reading aloud — a particularly effective memorisation technique for auditory learners.

1 and 2 Times Tables

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 and 4 Times Tables

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 and 6 Times Tables

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 and 8 Times Tables

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 and 10 Times Tables

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 and 12 Times Tables

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

Real-World Uses of Times Tables

Times tables are not an abstract school exercise — they appear constantly in daily life. Recognising these applications motivates learners of all ages to invest the practice time required for fluency.

Shopping and budgeting: "If each item costs £3 and I want 7, that's £21." Instant multiplication prevents over-spending and shortens checkout.
Cooking and recipes: Doubling or halving a recipe requires multiplying every ingredient. "The recipe serves 4 but I need 12 — multiply everything by 3."
Time management: "The film is 2 hours 15 minutes and I have 5 errands at 8 minutes each — is there time?" Quick multiplication estimates.
Sports statistics: Points per game × number of games played; miles per hour × hours driven.
DIY and construction: Area calculations ($ \text{length} \times \text{width} $) for flooring, tiling, and painting.
Understanding fractions and percentages: Simplifying $ \frac{24}{36} $ requires knowing that 24 = 6 × 4 and 36 = 6 × 6 — fluent times tables make this instant.
Algebra: Factorising $ x^2 + 7x + 12 $ needs you to recognise that 3 × 4 = 12 and 3 + 4 = 7. Times tables proficiency makes algebra dramatically easier.

Frequently Asked Questions

What are math times tables?

Math times tables are organised lists or grids showing the products of multiplying a given number (the multiplier) by each of the whole numbers from 1 to 12. A complete 12×12 times table chart shows all 144 multiplication facts in a single grid. They are also called multiplication tables, maths times, or times tables charts.

Which times tables should I learn first?

Begin with ×1, ×2, ×5, and ×10 — these have clear, obvious patterns. Move on to ×3, ×4, ×6, and ×9 once those are solid. Finish with ×7, ×8, ×11, and ×12, which require the most deliberate practice. This sequence means each new table builds on already-known facts rather than introducing everything at once.

How long does it take to memorise all times tables?

Most learners achieve full fluency with all 12 times tables in 6–12 weeks of consistent daily practice. Fifteen minutes a day of focused retrieval practice (quizzing yourself, not re-reading) is more effective than occasional long sessions. Children who practise daily typically outperform those who study only at homework time.

What is the quickest trick for the 9 times table?

Use the finger trick: hold all ten fingers out. To calculate 9 × n, fold down finger number n from the left. The count of fingers to the left gives the tens digit; the count to the right gives the units digit. Alternatively, remember that for 9 × n (where 1 ≤ n ≤ 10), the tens digit is (n − 1) and the units digit is (10 − n).

What is the commutative property and how does it help?

The commutative property states that $ a \times b = b \times a $. In a 12×12 times table chart, this means the grid is symmetric about the main diagonal. Every fact above the diagonal is mirrored below it. Because of this, a 12×12 chart contains only 78 unique facts rather than 144 — dramatically reducing how much you actually need to memorise.

What is the distributive property and how is it used in times tables?

The distributive property says $ a \times (b + c) = a \times b + a \times c $. This lets you split a hard fact into two easy ones. For example, $ 7 \times 8 = 7 \times (5 + 3) = 35 + 21 = 56 $. It is the mathematical foundation for tricks like "the 4s are double the 2s" ($ 4n = 2 \times 2n $) and "the 12s are the 10s plus the 2s" ($ 12n = 10n + 2n $).

Are there patterns I can use to learn times tables faster?

Yes — every table has at least one. The 2s are all even. The 5s end in 0 or 5. The 9s produce digit pairs summing to 9 (18, 27, 36…). The 10s just append a zero. The 11s repeat the single digit up to 9 (11×7=77). The 4s are double the 2s and the 8s are double the 4s. Recognising these patterns means you are using mathematical reasoning rather than pure memorisation.

How do I help my child learn times tables at home?

Keep practice sessions short (10 minutes maximum) and daily. Display a times table chart where your child studies. Use the Practice Quiz and Speed Test modes on He Loves Math for instant feedback. Test them casually at dinner or in the car — random retrieval practice is the single most powerful memory technique. Celebrate milestones: mastering each new table is a genuine achievement worth acknowledging.