Chinese Multiplication Method: The 9×9 Table Explained

The Chinese multiplication method is closely connected to the 9×9 multiplication table, known in Chinese as 九九乘法表 (jiǔ jiǔ chéng fǎ biǎo). Instead of learning multiplication only through repeated written calculations, Chinese students traditionally build fluency by memorizing multiplication facts from 1×1 through 9×9 and then applying these facts to mental math and multi-digit multiplication. This approach gives students a compact set of basic facts that can be recalled quickly.

In this guide, you will learn how the Chinese multiplication method works, what the Chinese multiplication table looks like, how Chinese students use multiplication facts, and why the 9×9 system is important in elementary mathematics.

What Is the Chinese Multiplication Method?

The Chinese multiplication method generally refers to the way multiplication facts and calculation strategies are taught in Chinese mathematics education. One of its most recognizable features is the 9×9 multiplication table, or 九九乘法表.

The basic idea is simple:

Memorize the multiplication facts from 1×1 to 9×9, then use those facts as building blocks for more complex calculations.

For example:

• 3 × 4 = 12
• 6 × 7 = 42
• 8 × 9 = 72

Once these facts become automatic, students can use them when multiplying larger numbers.

For example:

24 × 7

can be separated into:

20 × 7 + 4 × 7 = 140 + 28 = 168

The multiplication table provides the basic fact 4 × 7 = 28, while place-value reasoning handles the larger number.

Why Is It Called the 9×9 Multiplication Table?

The traditional Chinese multiplication table contains multiplication facts involving the numbers 1 through 9.

That creates a 9×9 grid of possible multiplication combinations:

Because multiplication is commutative, 3 × 7 and 7 × 3 have the same answer. Students therefore do not need to memorize every cell as a completely separate fact.

The Chinese 9×9 Multiplication Table

The Chinese multiplication table is called 九九乘法表 (jiǔ jiǔ chéng fǎ biǎo).

The name literally refers to the traditional sequence beginning with multiplication facts involving nine and ending with one, although modern educational materials often display it as a conventional 1–9 multiplication chart.

Here are the core multiplication facts:

The largest basic fact is therefore:

9 × 9 = 81

This is why the system is often described in English as the Chinese 9×9 multiplication table.

Chinese Multiplication Table in Chinese

Chinese multiplication facts are traditionally learned through short spoken phrases called 乘法口诀 (chéng fǎ kǒu jué), meaning multiplication rhymes or multiplication rules.

For example:

• 一一得一 — 1 × 1 = 1
• 一二得二 — 1 × 2 = 2
• 二二得四 — 2 × 2 = 4
• 三三得九 — 3 × 3 = 9
• 四五二十 — 4 × 5 = 20
• 七七四十九 — 7 × 7 = 49
• 八八六十四 — 8 × 8 = 64
• 九九八十一 — 9 × 9 = 81

The Chinese wording is short and rhythmic, which makes the facts easier to repeat aloud and memorize.

How Does the Chinese Multiplication Method Work?

The Chinese approach is not simply about memorizing a chart. The multiplication table becomes a foundation for mental calculation, written multiplication, division, fractions, and later algebra.

1. Learn Basic Multiplication Facts

Students first become familiar with multiplication facts within 9×9.

For example:

6 × 8 = 48

The goal is eventually to recall the answer without having to count groups of objects every time.

2. Use Patterns to Reduce Memorization

Multiplication contains many patterns.

For example, multiplying by 5 produces:

5, 10, 15, 20, 25, 30, 35, 40, 45

Multiplying by 9 produces:

9, 18, 27, 36, 45, 54, 63, 72, 81

Students can use these patterns as memory cues instead of treating every fact as unrelated.

3. Use Place Value for Larger Numbers

After basic multiplication facts become familiar, students combine them with place-value strategies.

For example:

23 × 4

can be calculated as:

20 × 4 + 3 × 4

= 80 + 12

= 92

The basic fact 3 × 4 = 12 is part of the calculation.

4. Apply Multiplication to Real Problems

Multiplication is then used in word problems and more advanced mathematics.

For example:

A box contains 8 rows of pencils with 6 pencils in each row. How many pencils are there?

Students can identify the multiplication relationship:

8 × 6 = 48

So there are 48 pencils.

Why Is the 9×9 Multiplication Table Important?

The 9×9 table gives students a relatively small set of multiplication facts that can be practiced until they become automatic.

This fluency can reduce the mental effort required for later calculations.

For example, when solving:

36 ÷ 6 = ?

a student who knows 6 × 6 = 36 can immediately identify the answer as 6.

This shows why multiplication and division are closely connected.

Chinese Multiplication Method vs. Other Ways of Learning Multiplication

The Chinese multiplication method is often associated with memorization and rapid recall, but effective multiplication instruction can include both conceptual understanding and procedural fluency.

These approaches do not have to compete with each other.

A student can first understand that 4 × 6 means four groups of six, then learn that 4 × 6 = 24, and eventually recall 24 automatically.

The strongest multiplication instruction generally connects meaning, patterns, and efficient calculation rather than relying on memorization alone.

How to Memorize the Chinese Multiplication Table

Children can use several strategies to learn the 9×9 multiplication table more efficiently.

Start With Easy Facts

Begin with multiplication facts involving:

• ×1
• ×2
• ×5
• ×10

Then move toward less familiar facts.

Use Commutative Pairs

Students only need to learn one relationship for each reversed pair.

For example:

3 × 8 = 24

means:

8 × 3 = 24

The two calculations have the same product.

Practice Difficult Facts Separately

Some facts may require more repetition, such as:

• 6 × 7 = 42
• 7 × 8 = 56
• 8 × 9 = 72
• 6 × 8 = 48

Instead of reviewing all 81 combinations equally, students can spend more time on facts they frequently forget.

Connect Multiplication With Division

Once students know:

7 × 8 = 56

they can also understand:

56 ÷ 7 = 8

and:

56 ÷ 8 = 7

This turns one multiplication fact into a related group of arithmetic facts.

FAQ About the Chinese Multiplication Method

1. What is the Chinese multiplication method?

The Chinese multiplication method commonly refers to learning multiplication through the 9×9 multiplication table (九九乘法表) and related calculation strategies. Students memorize basic multiplication facts and use them as foundations for mental math and more complex calculations.

2. What is the Chinese 9×9 multiplication table?

The Chinese 9×9 multiplication table contains multiplication facts from 1×1 through 9×9, with 9×9=81 as the largest basic fact. It is traditionally associated with the Chinese multiplication rhymes called 乘法口诀.

3. Is memorizing multiplication tables enough to learn multiplication?

No. Multiplication fluency is useful, but students also need to understand multiplication as equal groups, repeated addition, arrays, scaling, and other mathematical relationships. Fact recall works best as a foundation for conceptual understanding and problem solving.

Conclusion

The Chinese multiplication method is best understood as a combination of multiplication fact fluency, rhythmic memorization, number patterns, and practical calculation. At its center is the Chinese 9×9 multiplication table, or 九九乘法表, which gives students a compact foundation of facts from 1×1 to 9×9.

Learning the multiplication table can make mental math, division, multi-digit multiplication, fractions, and later mathematics more efficient. However, memorization works best when it is connected to mathematical meaning. Children should understand why multiplication works as well as recall what 7×8 equals.

For families looking to strengthen multiplication fluency and broader mathematical thinking, WuKong Math combines structured instruction, teacher guidance, and problem-solving practice. Parents can explore the program and try a free live math class before deciding whether the learning format fits their child.

James | WuKong Math Teacher

Graduated from Columbia University in the United States and has rich practical experience in mathematics competitions’ teaching, including Math Kangaroo, AMC 8… He teaches students the ways to flexible thinking and quick thinking in sloving math questions, and he is good at inspiring and guiding students to think about mathematical problems and find solutions.