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Math for Kids23 chapters | 325 lessons

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Instructor:
*Laura Pennington*

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

Once you know the underlying principle, diving with unlike denominators becomes easy. We'll learn how to divide fractions with unlike denominators, look at what's common between dividing fractions with like and unlike denominators, and see how they're applied in the world.

We want to know how to divide fractions with unlike denominators. Some of you may be familiar with dividing fractions that have like denominators by simply canceling out the denominators and dividing the numerators.

Well, as it turns out, this rule for dividing fractions with like denominators actually comes from the rule for dividing fractions in general. That is, there is a rule for dividing fractions regardless of if their denominators are the same or not!

To divide fractions, we need to now how to multiply fractions. Thankfully, multiplying fractions is probably the easiest operation to perform on fractions. To multiply fractions, we simply multiply their numerators together and multiply their denominators together, then simplify.

Pretty simple, wouldn't you agree? Well, the great news is that to divide fractions, we turn the division problem into a multiplication problem. To do this, we simply multiply the numerator of the division problem by the reciprocal of the denominator of the division problem.

Wait! What's that fancy word there? What the heck is a reciprocal? Don't worry! The **reciprocal** of a fraction has a fancy name, but is actually quite simple - it just interchanges the numerator and denominator of a fraction. That is, the reciprocal of the fraction *a*/*b* is *b*/*a*. See? Simple, right?

Okay, now that we've got all of our parts, let's put them together to see how to divide fractions with unlike denominators! Like we said, to divide fractions, we simply multiply the numerator by the reciprocal of the denominator.

We see that (*a*/*b*) / (*c*/*d*) = *a*/*b* * *d*/*c* = *ad*/*bc*. Now we can see where the rule for dividing fractions with like denominators comes from. Notice, if the denominators are the same, we have (*a*/*b*) / (*c*/*b*) = *a*/*b* * *b*/*c* = *ab* / *bc*. We see the *b* 's, or the denominators, cancel out to give *a*/*c*.

We see that dividing fractions with like or unlike denominators is actually the exact same process, and thankfully, the process is pretty easy!

To divide fractions with unlike denominators, we turn the division problem into a multiplication problem by multiplying the numerator of the division problem by the reciprocal of the denominator of the division problem, then we simplify.

Now that we know how to divide fractions with like or unlike denominators, let's consider an instance where knowledge of this process might come in handy! Let me start by asking if you have ever traveled with young children? If so, then you know that traveling with kids requires frequent stops to rest, eat, stretch, use the bathroom, let out some energy, and so on.

Imagine this: you are heading out on a road trip to visit family that is 322 2/5, or 1612/5, miles long. You've got kids in tow, so you decide to stop every 40 3/10, or 403/10, miles to make the trip more enjoyable for everyone.

Before you head out, you want to figure out how many stops there will be. You realize that figuring this out involves dividing the total number of miles of the trip (1612/5) by the length of the intervals between stops (403/10). Thankfully, you just got done reading this lesson a bit earlier, so you recognize that this is a matter of dividing fractions with unlike denominators! How exciting! You get to put something you learned into practice! You grab a pencil and start calculating!

We know we want to divide 1612/5 by 403/10. To do this, we know that we turn it into a multiplication problem by multiplying 1612/5 by the reciprocal of 403/10. Remember, the reciprocal of 403/10 is found by interchanging the numerator and denominator to get 10/403. Great! All we need to do is multiply 1612/5 by 10/403, and then simplify the answer.

We see that (1612/5) / (403/10) is 8. This tells us that you will be making 8 stops on your road trip. Time to pack up the kids and hit the road!

We see that division of fractions can easily come up in everyday life! Thankfully, this process is really just a matter of turning a division problem into a multiplication problem, by taking the **reciprocal** of the denominator, and then simplifying. Easy Peasy!

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Math for Kids23 chapters | 325 lessons

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