Multiplication Table — Complete Chart and Memorization Tips

See $7 \times 8$ and the answer $56$ should arrive before you finish reading it. That instant recall is the whole point of the multiplication table — a chart of the products of $1$ through $9$ that you read by crossing a row with a column.

The table and how to read it

Find the row for the first number, find the column for the second, and the intersection is your answer.

These are not just rhymes to recite. The same basic facts return in division, fractions, long multiplication, and mental math.

Why the table works — two ideas that cut the memory load

For positive integers, multiplication is "adding the same amount several times":

That is why every row has a steady rhythm. In the $6$ row the values are $6, 12, 18, 24, \ldots$, each step adding another $6$. Recognizing this pattern is more reliable than memorizing isolated facts.

The second idea is the commutative law $a \times b = b \times a$. Remembering "7 times 8 is 56" also means you have remembered "8 times 7 is 56," which is why the table is symmetric across the diagonal. Common memorization lists exploit this by including only non-repeating combinations:

• 1 times 1 is 1
• 1 times 2 is 2, 1 times 3 is 3, 1 times 4 is 4, 1 times 5 is 5, 1 times 6 is 6, 1 times 7 is 7, 1 times 8 is 8, 1 times 9 is 9
• 2 times 2 is 4, 2 times 3 is 6, 2 times 4 is 8, 2 times 5 is 10, 2 times 6 is 12, 2 times 7 is 14, 2 times 8 is 16, 2 times 9 is 18
• 3 times 3 is 9, 3 times 4 is 12, 3 times 5 is 15, 3 times 6 is 18, 3 times 7 is 21, 3 times 8 is 24, 3 times 9 is 27
• 4 times 4 is 16, 4 times 5 is 20, 4 times 6 is 24, 4 times 7 is 28, 4 times 8 is 32, 4 times 9 is 36
• 5 times 5 is 25, 5 times 6 is 30, 5 times 7 is 35, 5 times 8 is 40, 5 times 9 is 45
• 6 times 6 is 36, 6 times 7 is 42, 6 times 8 is 48, 6 times 9 is 54
• 7 times 7 is 49, 7 times 8 is 56, 7 times 9 is 63
• 8 times 8 is 64, 8 times 9 is 72
• 9 times 9 is 81

Worked example: finding $7 \times 8$ from the table

Look at the $7$ row on the left, then the $8$ column at the top. Trace the row across and the column down, and where they meet you read the value $56$:

If you prefer rhymes, match it directly to "7 times 8 is 56." There is a second fact you get for free along the way. By the commutative law, the swapped order gives the same product:

As long as the factors are the same, the product is unchanged even when the order is swapped. This is exactly why the table is symmetric across its diagonal — every entry above the diagonal has an identical twin below it, so reading $7 \times 8$ also hands you $8 \times 7$ at no extra cost.

Practice these, then check yourself

Answer $8 \times 6$ without looking. If it does not come instantly, do not force it — start from $8 \times 5 = 40$ and add one more $8$:

Then write out the full $6$ row or $7$ row from memory and verify each entry against the table above. Deriving the next answer from a known one (here, $6 \times 8 = 42 + 6 = 48$) sticks better than raw repetition.

Three tips that make recall easier:

• Start with the predictable rows. The $1$ row is the numbers themselves, the $2$ row is doubling, and the $5$ row always ends in $0$ or $5$.
• Use "one more step." If you know $6 \times 7 = 42$, then $6 \times 8 = 42 + 6 = 48$.
• Memorize only half. By $a \times b = b \times a$, you never need $3 \times 8$ and $8 \times 3$ as separate facts.

Calculation traps when learning the table

• Confusing multiplication with addition. $4 \times 6$ is not $4 + 6$; it means $6$ added $4$ times, so the result is $24$.
• Knowing the rhyme but freezing on the swap. If you know "6 times 7 is 42," you should immediately know $7 \times 6 = 42$.
• Memorizing every answer in isolation. This causes confusion in the $6$, $7$, and $8$ rows. Focus on how much each row increases by instead.

When you will use it

The table shows up most often in basic elementary arithmetic, but its usefulness goes far beyond recitation. When you do division, you often have to think backward — "what times what equals this number?" — and the table answers that instantly. When you simplify fractions, you lean again and again on the multiplication relationships between small integers. The same facts reappear inside long multiplication and everyday mental math.

When a problem's factors are small, retrieving the answer straight from the table is almost always faster than recalculating it from scratch. That speed is the real return on the effort of learning the table: a fact you can recall in a fraction of a second frees your attention for the harder parts of a problem. Treat the table as a network of patterns rather than a pile of isolated answers, and the $6$, $7$, and $8$ rows — the ones students most often stumble over — settle into place through the steady "add one more row value" rhythm.