A natural number is a common term in mathematics. It refers to numbers that are positive integers, including number 0. Natural numbers can’t be fractions of a number or have a decimal. Before we move on to the principles of multiplication of natural numbers, we need to have a good knowledge of the **multiplication table**.

The multiplication table includes multiplication results for numbers from 1 to 9.

The multiplication is a lot easier if you know the multiplication table.

Now, we can move on to the basics. The result of a multiplication of two numbers is called **a product**. The numbers we multiply are called **the factors**. The first factor is called the **multiplicand** and the second is called **multiplier**. The multiplication of one-digit numbers is the easiest form of multiplication and must be learned via the multiplication table before moving on to more complex examples. Now, we are going to look at multiplication of one-digit numbers with two-digit numbers.

Two-digit numbers are composed of “ones” and “tens”. For example, number 45 is made out of 5 “ones” and 4 “tens” because:

We are going to start with an example of multiplication of number 8 with 53:

We started by aligning the multiplier, number 6, with the “ones” number of the multiplicand, number 3.

Then we multiplied each digit of the multiplicand.

We wrote the “ones” digit of each product in the result. If the number has “tens” digit then it will be carried and added to the next product.

The process should look like this:

-> 3 times 6 is 18. Write 8 and carry the 1.

-> 5 times 6 is 30. 30 plus the carried 1 is 31.

-> The result is 318.

Now, we will move on to the __multiplication of two-digit numbers__.

Let’s take a look at the next example. We will multiply 71 with 56:

First we multiplied the “ones” digit, number 6, with 71 using the method shown before. The result is 426.

Now we multiply 5 with 71. The result is 355. Note that we shifted the result (355) one digit to the left, and a 0 is added at the end. The result is shifted because we multiplied the “tens” digit, number 5, with 71.

The process should look like this:

-> 6 times 1 is 6. Write 6.

-> 6 times 7 is 42. Write 42. Now we got the number 426.

-> 5 times 1 is 5. Write 5.

-> 5 times 7 is 35. Write 35. Now we got the number 355, and it is shifted by 1 digit to the left.

That means that *the last digit is 0*.

-> Now we need to add 426 to 3550 and the result is 3976.

Now we will take a look at multiplication of __two three-digit numbers__.

Let’s take a look at the next example. We will multiply 342 with 951:

The process of multiplying two three-digit numbers is almost the same as the multiplication of two-digit numbers.

The process should look like this:

-> 2 times 1 is 2. Write 2.

-> 2 times 5 is 10. Write 0, carry the 1.

-> 2 times 9 is 18 and plus carried the 1 it’s 19. The resulting number is 1902.

-> 4 times 1 is 4. Write 4.

-> 4 times 5 is 20. Write 0, carry the 2.

-> 4 times 9 is 36 and plus 2 it’s 38. The resulting number is 3804 and shifted 1 digit to the left by comparison to 1902.

-> 3 times 1 is 3. Write 3.

-> 3 times 5 is 15. Write 5, carry the 1.

-> 3 times 9 is 27 plus 1 is 28. The resulting number is 2853 and shifted one digit by comparison to number 3804.

-> After adding the numbers, we get the final result and that is 325242.

## Multiplication of natural numbers worksheets

Integers

**Two positive integers** (53.6 KiB, 406 hits)

**Three positive integers** (56.6 KiB, 352 hits)

**Four positive integers** (59.2 KiB, 336 hits)

**Two integers** (76.9 KiB, 390 hits)

**Three integers** (90.0 KiB, 343 hits)

**Four integers** (101.0 KiB, 358 hits)

Decimals

**Two positive decimals** (59.0 KiB, 384 hits)

**Three positive decimals** (64.1 KiB, 359 hits)

**Four positive decimals** (68.1 KiB, 371 hits)

**Two decimals** (88.9 KiB, 412 hits)

**Three decimals** (104.6 KiB, 342 hits)

**Four decimals** (121.0 KiB, 346 hits)

Fractions

**Two positive fractions** (148.3 KiB, 354 hits)

**Three positive fractions** (180.4 KiB, 333 hits)

**Four positive fractions** (209.8 KiB, 370 hits)

**Two fractions** (176.7 KiB, 417 hits)

**Three fractions** (211.4 KiB, 363 hits)

**Four fractions** (246.7 KiB, 323 hits)

Improper fractions

**Two positive improper fractions** (132.6 KiB, 332 hits)

**Three positive improper fractions** (162.4 KiB, 338 hits)

**Four positive improper fractions** (189.7 KiB, 335 hits)

**Two improper fractions** (163.5 KiB, 337 hits)

**Three improper fractions** (194.7 KiB, 381 hits)

**Four improper fractions** (226.5 KiB, 346 hits)