Charts

Multiplication Chart

A multiplication chart is a grid of products: find one number down the side and the other across the top, and the answer sits where the row and column meet. This page has an interactive times table you can set to 10, 12, 15 or 20, a printable 12 × 12 multiplication table, the patterns that make most rows easy, and the handful of facts worth drilling.

Printable multiplication chart 1–12

The chart below is the full 12 × 12 multiplication table: every product from 1 × 1 = 1 up to 12 × 12 = 144. It prints on a single page, so you can keep a copy on a desk, a fridge or the inside of a binder.

The interactive chart at the top of the page goes further. Set the size to 10, 12, 15 or 20 to redraw the grid, with the square numbers on the diagonal highlighted, or switch to One times table to list a single table, such as 7 × 1 = 7 through 7 × 12 = 84, as a column you can read aloud and learn. For products beyond the chart, the multiplication calculator shows the partial-product working for numbers of any size.

How to read a multiplication chart

A multiplication chart is a grid. The numbers across the top row and down the left column are the two numbers you multiply. Each cell holds the product of its row number and its column number.

1. Find the first number in the left-hand column.
2. Find the second number in the top row.
3. Run your finger along the row and down the column. The cell where they meet is the answer.

The terms multiplication chart, multiplication table and times table are used for the same grid. “The 7 times table” usually means a single row of it: 7, 14, 21 and so on up to 84.

Reading the chart backwards for division

Because division undoes multiplication, the same grid answers division facts. To find 56 ÷ 7, go to row 7, slide along until you reach 56, then look up to the top of that column: it is 8. This is the skill long division leans on at every step, so a reliable times table makes long division far less tiring. The division calculator checks any answer that falls outside the grid.

The chart is symmetric: 144 cells, 78 facts

Fold the chart along the diagonal that runs from the top-left corner to the bottom-right corner, and the two halves match. Row 3, column 8 holds 24; row 8, column 3 also holds 24. That mirror is the commutative property of multiplication: a × b = b × a. Order does not change a product.

This cuts the work of learning the table nearly in half. A 12 × 12 chart has 144 cells, but the 12 cells on the diagonal are each their own pair, and the other 132 cells come in 66 matching pairs. That leaves 78 different facts, not 144.

When you know 3 × 8, you already know 8 × 3. Say both out loud when you practise so the brain files them together.

Patterns in the times tables

Most of the chart is easier than it looks, because the rows follow patterns you can use instead of memorizing each fact cold.

Square numbers on the diagonal

The diagonal from top-left to bottom-right holds the perfect squares: a number times itself. On a 12 × 12 chart they are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144. The gaps between them are the odd numbers in order, which gives you a way to rebuild a square you have forgotten.

If you know 7 × 7 = 49, then 8 × 8 = 49 + 15 = 64. The square root calculator runs the other way, taking 64 back to 8.

The 9s trick

Nine is one less than ten, so 9 × n = 10 × n − n. For 9 × 7 that is 70 − 7 = 63. Two more checks fall out of that. Up to 9 × 10, the tens digit of the answer is one less than the number you multiplied by, and the two digits add up to 9: 9 × 7 = 63, and 6 + 3 = 9.

The finger version: hold up ten fingers and fold down the one you are multiplying by, counting from the left. For 9 × 7, fold down the seventh finger. Six fingers stand to its left (the tens) and three to its right (the ones): 63.

The 5s and the 10s

Every multiple of 10 ends in 0: you write a zero after the number. Every multiple of 5 ends in 5 or 0, and a 5s fact is half the matching 10s fact. 5 × 7 is half of 70, which is 35. If the other number is even, the answer ends in 0; if it is odd, it ends in 5.

The 11s

From 11 × 1 to 11 × 9 you repeat the digit: 11 × 4 = 44, 11 × 8 = 88. The last three need one idea. Multiplying by 11 is multiplying by 10 and adding the number once more, so 11 × 12 = 120 + 12 = 132. The same idea gives 11 × 10 = 110 and 11 × 11 = 121.

The 12s

Split 12 into 10 + 2. Multiply by 10, multiply by 2, add the two results. 12 × 7 = 70 + 14 = 84 and 12 × 8 = 80 + 16 = 96. That split is the distributive property at work, and it is the same trick that turns any awkward fact into two easy ones.

Doubling: the 2s, 4s and 8s

The 2s are doubles. The 4s are doubles of the 2s, and the 8s are doubles of the 4s. To get 8 × 7, double 7 three times: 14, 28, 56.

The 6s with an even number

When you multiply 6 by an even number, the answer ends in the same digit as that number: 6 × 2 = 12, 6 × 4 = 24, 6 × 6 = 36, 6 × 8 = 48. The tens digit is half the number you multiplied by. It is a quick self-check for the row that trips people up most.

Odd and even products

A product is odd only when both numbers are odd. On the 12 × 12 chart, 6 rows and 6 columns are odd, so 6 × 6 = 36 of the 144 cells are odd and the other 108 are even. If you multiply two numbers and one is even but your answer is odd, something has slipped.

What else the chart shows

The grid is a reference for more than single-digit products.

• Factors. Every cell where a number appears gives a factor pair. 36 appears five times on the 12 × 12 chart: 3 × 12, 4 × 9, 6 × 6, 9 × 4 and 12 × 3. The factor calculator lists every pair for numbers beyond the grid.
• Common multiples. Each row is a list of multiples. Rows 4 and 6 both contain 12, 24 and 36, and 12 is the first they share, which is their least common multiple. The LCM calculator does the same job for larger numbers.
• Equivalent fractions. Put one row over another and read across. Rows 3 and 4 give 3/4, 6/8, 9/12, 12/16 and so on: every pair is the same fraction. The guide to equivalent fractions builds on exactly this.
• Square roots. Find a number on the diagonal, and its row number is the square root. 81 sits at row 9, column 9.

The facts people find hardest

Strip out everything the patterns cover and very little is left. Of the 78 different facts on a 12 × 12 chart, those involving 1, 2, 5, 10 or 11 follow simple rules. That leaves 28. Remove the squares and the 9s, and 15 remain. If the 3s and 4s are already solid, only six facts are left:

These are the ones to drill. A memory hook helps with 7 × 8: write 56 = 7 × 8 and you read the digits 5, 6, 7, 8 in order. The neighboring squares 7 × 7 = 49 and 8 × 8 = 64 are worth anchoring too, because once they are fixed, 6 × 7, 6 × 8 and 7 × 8 can each be reached from a square in one step.

Tips for memorizing the times tables

1. Learn in order of difficulty, not 1 to 12. Start with 1, 2, 5 and 10, then 11 and the squares, then 9, 3 and 4. Leave the 6s, 7s, 8s and 12s for last, because by then most of their facts are already known from the other direction.
2. Practise one table at a time. Use the One times table mode in the chart above to list a single row, read it aloud, then cover the answers and recite it.
3. Count by the number. Skip counting (7, 14, 21, 28…) builds the row as a sequence, so a forgotten fact can be rebuilt from the one before it.
4. Practise in short, frequent sessions. A few minutes most days works better than one long session a week.
5. Mix the order. Once a table is solid in order, test it shuffled. Knowing that 7 × 6 comes after 7 × 5 is not the same as knowing 7 × 6 on its own.
6. Focus on what you miss. Keep a short list of facts you got wrong and practise only those until they stick.
7. Use the patterns to check. The 9s digit sum, the 5s ending in 0 or 5, and the odd/even rule all catch slips on the spot.

Multiplication chart to 15 and 20

A 12 × 12 chart covers the facts most schools expect, but larger grids are useful for the 13s through 20s and for spotting more squares. Set the chart above to 15 or 20. A 20 × 20 chart has 400 cells and runs up to 20 × 20 = 400.

You do not need to memorize the larger rows. Split them with the distributive trick instead: 15 × 12 = 10 × 12 + 5 × 12 = 120 + 60 = 180, and 14 × 12 = 140 + 28 = 168. The squares from 13 to 20 are worth knowing, because they come up often: 169, 196, 225, 256, 289, 324, 361 and 400.

Common mistakes

• Reading the wrong row or column. On a printed chart it is easy to slide one line off. Use a ruler or two fingers, and check the answer against a pattern.
• Confusing neighbors. 6 × 8 and 7 × 7 differ by 1, and 6 × 9 and 7 × 8 differ by 2. Rebuild from a fact you trust rather than picking between them.
• Treating 8 × 3 and 3 × 8 as separate facts. They are the same product; learn them together.
• Adding instead of multiplying. 6 × 6 is 36, not 12. Saying “six sixes” instead of “six times six” keeps the meaning clear.
• Forgetting the zero row. Most charts start at 1, but any number times 0 is 0, and 0 never appears on the grid as a factor.

Frequently asked questions

Calculators for this

Every one of these shows the working, so you can check the method as well as the answer.

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