# Three multiplications of a fraction by a whole number where the answer is 4

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Three multiplications of a fraction by a whole number equals 4. I will choose `1/2` to be my fraction. X is a whole number that we will solve for.``

`1/2 * 1/2 * 1/2 * x = 4`

`1/8 * x = 4`

`x = 32`

When you multiply 32 by `1/2` 3 times the result is 4.

You can pick any combination of a fraction and a whole number where the numerator of the fraction is 1 and the whole number is the 4th multiple of the denominator.

For example, 8 is the 4th multiple of 2: 8 = 2*4, so

`1/2 * 8 = 1/2* 8/1 = 4`

Or, 12 is a 4th multiple of 3:

`1/3 * 12 = 1/3*12/1 = 4`

Or, 20 is a 4th multiple of 5:

`1/5*20 = 1/5*20/1 = 4`

You can take any fraction you want and multiply the denominator by 4, since you want the total to equal 4. With that, you can then take that fraction that you have created by multiplying the denominator by four and creating the **reciprocal** of that.

A **reciprocal **means that you take one fraction and flip the numerator and denominator. Here's an example:

`1/2` you flip the numerator and denominator and get `2/1` , or `2`

In this case, you will then have to multiply this original fraction that you chose with this reciprocal of the original fraction with the denominator multiplied by 4.

Here's one.

We can choose 1/4, for example.

`1/4` multiply denominator by 4 `1/16` reciprocal = `16/1`

`16/1*1/4=16/4, or 4.`

Now, you said **whole** number. If you're wondering what the whole number is, it is simply the fraction with a denominator of 1. So,

`16/1=16`

Here's more examples

`1/6*24/1=4`

`1/2*8/1=4`

Hope I helped!

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