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

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*5= 375`

Which is the same as:

`5x= 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 (`5x= 375`) by 5, which looks like this:

`5x= 375`

=`(5x)/5= 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*20= 100`

and that:

`5*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(20+5)= (100+25)`

This means that:

`5*25= 125`

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

`375/125= 3`

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

`25*3= 75`

And there you have it! I hope that helped!

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

The formula: `x*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*5/ 5``=``375/5`

`x=375/5`
So our answer is `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