# How to Use the Fractional-Part-of-a-Number Equation

Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

This lesson will cover how to use the fractional part of a number equation. We will see how to set up this equation and how to use this equation to find the fractional part of a number. We will use real world examples to illustrate this process.

## Fractional Part of a Number Equation

Have you ever noticed how expensive cell phones can be? It's always a great day when we find a good deal on a new cell phone! Suppose Frank is talking to his friend Stacy, and he is bragging about getting a great deal on a new phone he just bought. He tells her that he got it for 3/4 of the normal price, which was \$372. Well, it sounds like Frank got a good deal! However, we don't know how much he actually paid!

Figuring this out involves finding the fractional part of a number. To find what Frank paid for the phone, we would want to find 3/4 of 372. In other words, we need to ask 'what is 3/4 of 372?', and it turns out that, when worded this way, this particular question can be transformed into the fractional part of a number equation. This equation allows us to find the fractional part of a number.

In general, to convert the question 'what is a/b of c?' to this equation, we replace the word 'what' with a variable, say x, because this is going to be what we are trying to find. Next, we convert the word 'is' to the equal sign, and lastly, we convert the word 'of' to multiplication.

All together this gives that the question 'what is a/b of c?' is equivalent to the equation x = (a/b) × c. This equation is the fractional part of a number equation.

Let's go ahead and convert our question, 'what is 3/4 of 372?', into an equation, so we can use the equation to find out what Frank paid for the phone. We convert 'what' to x, is to =, and 'of' to ×.

We get that x = (3/4) × 372. Great! We can use this to find out what Frank paidâ€¦we just need to figure out how to do that!

## Using the Fractional Part of a Number Equation

Once we have our fractional part of a number equation:

x = (a/b) × c

we just need to know how to calculate (a/b) × c, in order to solve for x. This may look complicated, but it's actually just a matter of multiplication and division! To multiply a fraction, a/b, by a number c, we follow these steps:

1. Multiply a × c.
2. Divide the result by b.

Well, that's not complicated at all! Let's find out what Frank is bragging about! We just need to find (3/4) × 372. First, we multiply 3 by 372.

3 × 372 = 1116

Now, we just divide the result by 4.

1116 / 4 = 279

We get that 279 is 3/4 of 372, so Frank paid \$279 for his phone. Stacy laughs and says that's nothing - she got the exact same phone for 3/5 of what Frank paid for it.

Oh goody! Another opportunity to practice using these equations! Let's find out what Stacy paid for her phone. In other words, we want to answer the question 'what is 3/5 of 279?'. First, we convert the question into equation form.

We get the equation x = (3/5) × 279. All we have to do now is find (3/5) × 279. First, we multiply 3 by 279.

3 × 279 = 837

Then, we divide the result by 5.

837 / 5 = 167.4

It looks like 3/5 of 279 is 167.40, so Stacy paid \$167.40 for the phone. That's a really good deal! Looks like Stacy has earned bragging rights over Frank.

This process is actually pretty easy! Let's consider one more example, just for good measure.

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