Welcome to Mathnasium’s Math Tricks series. Today we are finding the value of the whole, given the value of a fractional part in a Wholes and Parts problem.

In an earlier Mathnasium Math Trick we defined the *numerator* and *denominator* of a fraction. To find the value of the whole when the numerator of the given fraction is 1, we multiply the denominator by the value of each part.

To find the value of the whole when the numerator is greater than 1, we use the following steps:

- Find the value of each part by dividing the total value of the given parts by the numerator.
- Multiply the number from Step 1 by the denominator.

Follow the example below to find the whole.

##### Example: 5⁄12 of ____ = 20.

Step 1: Find the value of each part by dividing the total value of the given parts by the numerator.

Since the 5 equal parts of the whole have a total value of 20, the value of each part is 4.

Alternatively, the total value of the given parts, 20, divided by the numerator, 5, is equal to 4.

Step 2: Multiply the number from Step 1 by the denominator.

Multiplying the value of each equal part (4) by the total number of parts in the whole (12), we get 48.

Answer: 48.

Now, with this strategy, you are ready to use this Mathnasium Math Trick to find the value of the whole, given the value of a fractional part. Click here for more practice problems, then check your answers here.

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