# Multiplication Calculator

By Maciej Kowalski, PhD candidate
Last updated: Sep 09, 2021

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 or partial products 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.

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`,

`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.

Maciej Kowalski, PhD candidate
result = a₁ * a₂
Multiply...
two numbers.
Factors
a₁
a₂
Result
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