So think of the next number after 14 that ends with 1, which is 21. The next number in the direction of the arrow is 1.So think of the next number after 7 that ends with 4, which is 14. The next number in the direction of the arrow is 4.Look at the 7 in the first picture and follow the arrow.

The pattern also works with multiples of 10, by starting at 1 and simply adding 0, giving you 10, then just apply every number in the pattern to the 'tens' unit as you would normally do as usual to the 'ones' unit.įor example, to recall all the multiples of 7: As you would start on the number you are multiplying, when you multiply by 0, you stay on 0 (0 is external and so the arrows have no effect on 0, otherwise 0 is used as a link to create a perpetual cycle). These patterns can be used to memorize the multiples of any number from 0 to 10, except 5. Figure 2 is used for the multiples of 2, 4, 6, and 8. Some schools even remove the first column since 1 is the multiplicative identity.Ĭycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypadįigure 1 is used for multiples of 1, 3, 7, and 9. In China, however, because multiplication of integers is commutative, many schools use a smaller table as below. The illustration below shows a table up to 12 × 12, which is a size commonly used nowadays in English-world schools. Leslie also recommended that young pupils memorize the multiplication table up to 50 × 50. In his 1820 book The Philosophy of Arithmetic, mathematician John Leslie published a multiplication table up to 99 × 99, which allows numbers to be multiplied in pairs of digits at a time. In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were 'a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144.' Modern times

The Greco-Roman mathematician Nichomachus (60–120 AD), a follower of Neopythagoreanism, included a multiplication table in his Introduction to Arithmetic, whereas the oldest surviving Greek multiplication table is on a wax tablet dated to the 1st century AD and currently housed in the British Museum. It is also called the Table of Pythagoras in many languages (for example French, Italian and Russian), sometimes in English. The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC).

Multiplication chart for 8