# Five times a number is 375. What is the number?

Apr 7, 2016

75.

#### Explanation:

So the first part of the question: "Five times a number is 375." is actually saying: "Some number multiplied by 5 is equal to 375", which looks like this:

$x \cdot 5 = 375$

Which is the same as:

$5 x = 375$

The second part of the problem: "What is the number?" tells us that they want us to solve for $x$. We can do this by dividing both sides of our equation ($5 x = 375$) by 5, which looks like this:

$5 x = 375$

=$\frac{5 x}{5} = \frac{375}{5}$

Lucky for us 375 is divisible by 5 (the divisibility rule for 5 states: any number is divisible by 5 if it ends in a 0 or 5) which means we will get a whole number as opposed to a fraction or decimal.

We can solve this with mental math if we remember that:

$5 \cdot 20 = 100$

and that:

$5 \cdot 5 = 25$

If we add the 20 and the 5 together we get 25:

$20 + 5 = 25$

Now if we multiply 25 by 5 we get 125 (This is the same as adding 100 and 25!). So this means that:

$5 \left(20 + 5\right) = \left(100 + 25\right)$

This means that:

$5 \cdot 25 = 125$

125 just so happens to be 3 times smaller than our target number:

$\frac{375}{125} = 3$

This means that we can multiply 25 by 3 to solve for $x$.

$25 \cdot 3 = 75$

And there you have it! I hope that helped!

Jun 27, 2017

$75$ is the number and see below for the procedure!

#### Explanation:

Well, using algebra for these kind of problems might save you more time than guessing! So let's start, shall we?

The formula: $x \cdot 5 = 375$
Now, lets leave $x$ on one side and also get our answer by taking $5$ to the other side. We are going to do that by dividing both sides by $5$! If you do something to one side, then you have to do it to the other! That will eliminate the $5$ on left side and add 5 on the right side.

$x \cdot \frac{5}{5}$$=$$\frac{375}{5}$

$x = \frac{375}{5}$
So our answer is $\frac{375}{5}$! Wait a second... oh yes, we have one more step to do in order to finish this equation! We have to simplify it! $5$ can go into $375$ so you can divide that!

$x = 75$!

There, now we have our final answer!
My source is my mind!

-Moksha