What is 7 × 8?
- Split the 8
- Double twice
Answer
The one most people find hardest. Some remember it as 5, 6, 7, 8 — because 56 = 7 × 8.
Multiplication chart
One to twelve. Tap a square, or print it clean.
- Free
- No account
- Every step shown
- Arithmetic to calculus
Solution
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Answer
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The chart below runs from 1 to 12 in both directions. Find one number along the top and the other down the side, and the answer is where they meet — and because multiplication is commutative, it does not matter which one you pick first. Tap any square to read it out. The page prints without the menus, so it works on a wall.
The tricks worth knowing
There are 144 squares but far fewer facts to learn, because most of them come free.
Order does not matter
7 × 8 and 8 × 7 are the same square reflected across the diagonal, so learning one gives you the other. That halves the table straight away.
The nines trick
For 9 × n, the digits always add to 9, and the first digit is n − 1. 9 × 7: first digit 6, and 6 + 3 = 9, so 63.
The hard ones are few
Once 0, 1, 2, 5, 10 and 11 are free, and the diagonal is learned, the genuinely hard facts are 6×7, 6×8, 7×8, 7×9 and 8×9. Five facts, not 144.
Read it backwards for division
The chart is a division table too. To find 56 ÷ 7, look along row 7 for 56 and read the column heading: 8.
Worked examples
Each one is solved the way the solver solves it: the rule first, then the line.
What is 12 × 12?
- Split into tens and twos
- Add the parts
Answer
What is 144 ÷ 12?
- Ask what times 12 gives 144
- Read it off the chart
Answer
What are the factors of 36?
- Find every pair that multiplies to 36
- List them in order
Answer
36 appears four times in the chart, once for each pair that is inside 12 × 12.
Where marks get lost
Learning all 144 squares
The table is symmetric, so half of it is a reflection, and the 0, 1, 2, 5 and 10 rows are free. Learning the five genuinely hard facts is most of the work.
Confusing 6 × 7 and 6 × 8
42 and 48 sit next to each other and swap constantly. 6 × 8 is even in both digits going up by two: 48. 6 × 7 is 42.
Reading the wrong row
On a grid this size it is easy to slide up or down a line. Tapping the square highlights the exact one, which is what the readout under the chart is for.
Questions
How do I use a multiplication chart?
Find one number along the top row and the other down the first column. The answer is the square where they meet. Either order gives the same square.
How do I remember the 9 times table?
The digits of every answer add to 9, and the tens digit is one less than the number you multiplied by. 9 × 6: tens digit 5, and 5 + 4 = 9, so 54.
Can I use it for division?
Yes. Find the answer inside the row of the number you are dividing by, then read the column heading. 56 in row 7 sits under 8, so 56 ÷ 7 = 8.
Why is the chart symmetric?
Because multiplication is commutative: a × b always equals b × a. The diagonal is the mirror line, and it holds the square numbers.
What are the square numbers on the chart?
The diagonal from top left to bottom right: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. They are highlighted, and they are the numbers with an odd count of factors.
Which multiplication facts are hardest?
Once the easy rows are free, five remain: 6×7, 6×8, 7×8, 7×9 and 8×9. Almost every mistake in the table is one of these.
Can I print it?
Yes. The page prints the chart alone, without the menus or the colour fills, so it stays readable in black and white.
Why stop at 12?
Twelve is where school tables stop and where the useful facts run out. Above that, split the number instead: 15 × 7 is 10 × 7 plus 5 × 7.