# Multiplication facts

The multiplication facts are the multiplication problems formed by multiplying all the combinations of the numbers 1 through 10. For example, 1 × 1 = 1, 2 × 7 = 14, and 10 × 10 = 100 are all multiplication facts. Using the numbers 1-10, there are 100 multiplication facts. If we were to include 0, there would be 121, but most multiplication charts don't include 0, since multiplying anything by 0 results in 0.

Below is a multiplication chart for the integers 1-10, which can be used as a reference for all the multiplication facts.

 × 1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100

Learning the multiplication facts is an essential part of early mathematics. Without knowing the multiplication facts, things like long division, finding the common denominator of a fraction, and many other math problems would be more difficult and time consuming. As such, learning/memorizing the multiplication facts is one of the earliest things taught in mathematics.

## Learning the multiplication facts

Using the numbers 1-10, there are 100 multiplication facts. Using properties of multiplication, it is possible to significantly reduce the number of facts that need to simply be memorized. For example, referencing the multiplication chart above, it is only necessary to memorize the cells shaded in green, along with everything below (or above) those cells. This is because of the commutative property of multiplication, which states that

a × b = b × a

This means that if we know that 4 × 6 = 24, we also know that 6 × 4 = 24, so we only need to memorize one of those multiplication facts to know the result of both.

We can also use the identity property of multiplication to further reduce the number of multiplication facts we need to memorize. The identity property of multiplication states that

1 × a = a

This means that no matter what we multiply a by 1, the result will be a.

Another way to reduce the number of facts we need to memorize is understanding that multiplying any integer by 10 results in that same number with an added 0. This is due to the fact that we use a decimal numeral system.

Taking all of the above into consideration, there are 36 multiplication facts that require rote memorization, as shown in the multiplication chart below.

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