# Multiplication Calculator

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`

times `7`

(written `16 * 7`

) is the same as adding `16`

seven times, or, equivalently, adding `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.

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

## Product or multiplication: how to multiply numbers

**Product** and **multiplication** are the same things: they 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`

times `5`

means that we add `24`

five times, i.e.,

`24 * 5 = 24 + 24 + 24 + 24 + 24 = 120`

.

Similarly, `12`

times `20`

translates to adding `12`

twenty times:

`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`

times `5`

can also mean adding `5`

twenty-four times:

`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`

times `20`

by adding `20`

twelve times:

`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.

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`

, `18`

, or `2020`

. We've learned how to multiply those and what, say, `16`

times `7`

is, but how do we find the product of decimals? For example, what is `0.2`

times `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,

`0.2 * 1.25 = (2/10) * (125/100) = (2 * 125) / (10 * 100) = 250/1000 = 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`

and `1.25 = 5/4`

, so

`0.2 * 1.25 = (1/5) * (5/4) = (1 * 5) / (5 * 4) = 5/20 = 1/4`

.

**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`

and `1.25`

, we can begin by **forgetting the dots**. That means that to find `0.2 * 1.25`

, we start by finding `2 * 125`

, which is `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`

and two in `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`

, which gives `0.250 = 0.25`

(we write `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`

**times** `12`

with the multiply calculator. At the top of our tool, we see the formula:

`result = a₁ * a₂`

.

This means that to calculate `2020 * 12`

, we need to input:

`a₁ = 2020`

and `a₂ = 12`

.

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

`result = 2020 * 12 = 24240`

However, say that you'd like to **multiply the result further** by `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 `a₁ = 24240`

and `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 `a₁`

, `a₂`

, `a₃`

, and so on up to `a₁₀`

(note how initially only `a₁`

and `a₂`

are there, but more variables appear once you start filling the fields). It's then enough to input:

`a₁ = 2020`

, `a₂ = 12`

, `a₃ = 1.3`

,

and read off the answer from underneath:

`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`

like we did in the first section? We, for one, don't.