Welcome to Omni's **multiplication calculator**, where we'll study one of the four basic arithmetic operations: **multiplication**. In short, we use it whenever we want to add the same number several times. For instance, $16$16 times $7$7 (written $16 \times 7$16×7) is the same as adding $16$16 seven times, or, equivalently, adding $7$7 sixteen times. Conveniently, our tool works also as a **multiplying decimals calculator**. What is more, even if you have more than two numbers to multiply, you can still find their product with this calculator.

**Note**: If you'd like to see step-by-step solutions to multiplying large numbers, check out Omni's long multiplication calculator or partial products calculator.

Let's waste not a second more and see **how to multiply numbers**!

## How do I multiply numbers?

**Product** and **multiplication** refer to the same thing: the result from multiplying numbers (or other objects, for that matter). Fortunately, the process is very simple: it boils down to adding the value a suitable number of times. For instance, $24$24 times $5$5 means that we add $24$24 five times, i.e.:

$\begin{split}24& \times 5 \\&= 24 + 24 + 24 + 24 + 24 \\&= 120\end{split}$24×5=24+24+24+24+24=120

Similarly, $12$12 times $20$20 translates to adding $12$12 twenty times:

$\begin{split}12 &+ 12 + 12 + 12 + 12 + 12 \\&+ 12 + 12 + 12 + 12 + 12 \\&+ 12+ 12 + 12 + 12 + 12 \\&+ 12 + 12 + 12 + 12 = 240\end{split}$12+12+12+12+12+12+12+12+12+12+12+12+12+12+12+12+12+12+12+12=240

However, note that **we can always invert the process** of finding the product with multiplication. In other words, the $24$24 times $5$5 can also mean adding $5$5 twenty-four times:

$\begin{split}5& + 5 + 5 + 5 + 5 + 5 + 5 \\&+ 5 + 5 + 5 + 5 + 5 + 5 \\&+ 5 + 5 + 5 + 5 + 5 + 5 \\&+ 5 + 5 + 5 + 5 + 5 = 120\end{split}$5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5=120

and we can get $12$12 times $20$20 by adding $20$20 twelve times:

$\begin{split}20 &+ 20 + 20 + 20 + 20 + 20\\ &+ 20 + 20 + 20 + 20 + 20 \\&+ 20 = 240\end{split}$20+20+20+20+20+20+20+20+20+20+20+20=240

It's always our choice how to multiply the numbers since **the result is the same either way**. In mathematical terms, this means that the product or multiplication is **a commutative operation**. Note that the same is true for addition. On the other hand, it does not hold for, say, subtraction.

🔎 Do you know that there are more ways to write arithmetic operations than the "classic" **operator in the middle** one? Try them out with our Polish notation converter!

Also, **our multiply calculator only deals with numbers**, but mathematicians figured out how to multiply other objects. Below we list a few other multiplication calculators from Omni.

- Matrix multiplication calculator;
- Multiplying fractions calculator; and
- Multiplying radicals calculator.

However, **it's not always that we deal with integers** like $2$2, $18$18, or $2020$2020. We've learned how to multiply those and what, say, $16$16 times $7$7 is, but how do we find the product of decimals? For example, what is $0.2$0.2 times $1.25$1.25? Is our multiplication calculator also **a multiplying decimals calculator**?

**Oh, you bet!**

## Multiplying decimals

In essence, **decimals are fractions**. Therefore, one way of multiplying decimals is to convert them to regular fractions and then use the basic rule of *numerator times numerator over denominator times denominator*. For example,

$\begin{split}0.2\times1.25 &= \frac{2}{10}\times \frac{125}{100} \\[1em]&= \frac{2 \times 125}{10\times 100} \\[1em]&=\frac{250}{1000} = 0.25\end{split}$0.2×1.25=102×100125=10×1002×125=1000250=0.25

Of course, we could have also found easier equivalent fractions to the two given before multiplying. In this case, we could have said that $0.2 = 1/5$0.2=1/5 and $1.25 = 5/4$1.25=5/4, so

$\begin{split}0.2 \times 1.25 &=\frac 1 5 \times \frac 5 4 \\[1em]&= \frac{1\times 5}{5\times 4}\\[1em]&= \frac{5}{20} = \frac 1 4\end{split}$0.2×1.25=51×45=5×41×5=205=41

**Both answers are correct**; it's always your choice how to multiply decimals. However, besides the two mentioned, **there is another**.

When multiplying decimals, say, $0.2$0.2 and $1.25$1.25, we can begin by **forgetting the dots**. That means that to find $0.2 \times 1.25$0.2×1.25, we start by finding $2 \times 125$2×125, which is $250$250. Then we count how many digits to the right of the dots we had in total in the numbers we started with (in this case, it's three: one in $0.2$0.2 and two in $1.25$1.25). We then **write the dot that many digits from the right** in what we obtained. For us, this translates to putting the dot to the left of $2$2, which gives $0.250 = 0.25$0.250=0.25 (we write $0$0 if we have no number in front of the dot).

All in all, we've seen **how to multiply decimals in three ways**. To be perfectly honest, the first two were pretty much the same thing; it's just that the intermediate steps were in a different order. Nevertheless, this concludes the part about how to multiply without a calculator. Now let's describe in detail how to do it with one, and to be precise, **with Omni's multiplication calculator**.

## Example: using the multiplication calculator

**Let's find** $2020$2020 **times** $12$12 with the multiply calculator. At the top of our tool, we see the formula:

$\mathrm{Result} = a_1\times a_2$Result=a1×a2

This means that to calculate $2020 \times 12$2020×12, we need to input:

$a_1 = 2020$a1=2020

And:

$a_2 = 12$a2=12

The moment we give the second number, **the multiplication calculator spits out the answer** in the *Result* field.

$\mathrm{Result} = 2020\times 12=24240$Result=2020×12=24240

However, say that you'd like to **multiply the result further** by $1.3$1.3 (remember that our tool also works as a multiplying decimals calculator).

We could just clear out the fields and write the answer from above into one of the factors, i.e., input $a_1 = 24240$a1=24240 and $a_2 = 1.3$a2=1.3. Alternatively, we can simply select *many numbers* under *Multiply...*, which lets us **find the product of multiplication for more numbers**. If we do so, we'll get the option to input $a_1$a1, $a_2$a2, $a_3$a3 and so on up to $a_{10}$a10 (note how initially only $a_1$a1 and $a_2$a2 are there, but more variables appear once you start filling the fields). It's then enough to input:

$\begin{split}a_1&=2020\\a_2&=12\\a_3&=1.3\end{split}$a1a2a3=2020=12=1.3

And read off the answer from underneath:

$\begin{split}\mathrm{Result} &= 2020\times 12 \times 1.3 \\&= 31512\end{split}$Result=2020×12×1.3=31512

Well, this multiply calculator sure saves a lot of time. Can you imagine **writing two thousand twenty times** the number $12$12 like we did in the first section? We, for one, don't.

## FAQ

### Is product same as multiplication?

**Multiplication** is one of four basic arithmetic operations (the three others are addition, subtraction, and division).

**Product** is the result of carrying out multiplication: when we multiply two numbers (multiplicand and multiplier), we obtain their product.

### What are the parts of multiplication?

The two numbers we multiply together are called multiplicands and multipliers or just factors. The result of the multiplication is called the product. For instance, in the multiplication problem `3 × 5 = 15`

, the number `3`

is the multiplicand, `5`

is the multiplier, both `3`

and `5`

are the factors, and `15`

is the product.

### What are the properties of multiplication?

The arithmetic operation of multiplication of two numbers is:

- Associative;
- Distributive; and
- Commutative.

### What is the neutral element of multiplication?

The neutral element (a.k.a. identity element) of multiplication is the number `1`

. This means that `1`

is the (unique) number such that when we multiply any number by `1`

then we obtain the same number we started with.

### How do I multiply by 100?

To multiply any number by `100`

, follow these steps:

- If your number is an integer, write two additional zeros at the right end of your number.
- If your number has a decimal point, you'll need to move the decimal point two places to the right. Add one or two trailing zeros if there are less than two decimal digits.