Dividing Fractions and Mixed Numbers

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  • 0:05 Let's Divide
  • 0:33 Dividing Fractions
  • 1:08 Practice Dividing Fractions
  • 3:10 Dividing Mixed Numbers
  • 4:09 Practice Dividing…
  • 6:47 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Dividing fractions and mixed numbers? It sounds daunting, but it's not as tricky as it sounds. In this lesson, we'll learn how to divide fractions and mixed numbers.

Let's Divide

Let's talk about cookies. Baking cookies is a form of chemistry - tasty, sometimes chocolate chip chemistry. But, there also seems to be an awful lot of math involved. This is especially true if you're like me and you don't always have an unlimited supply of every ingredient.

For example, maybe you have only 1 1/2 cups of flour left and you need to modify your recipe so that you maximize your cookie potential. You're going to need to divide fractions. Let's learn more about this critical skill.

Dividing Fractions

To divide fractions, we follow three steps. Step one: flip the second fraction. This gives you its reciprocal. Step two: multiply the fractions. This means you multiply the numerators, then the denominators. Finally, step three: simplify as needed.

So, with 9/10 divided by 4/5, we flip the 4/5 to get 5/4. That's its reciprocal. Then, we multiply. 9 * 5 is 45, and 10 * 4 is 40. So, 45/40. We simplify that to 9/8, or 1 1/8.

Practice Dividing Fractions

Let's try a few in context. Let's say you're throwing a party. You have a punch bowl that has 8/9 of a gallon of punch left. If your cups will hold one cup of punch, which is 1/16 of a gallon, how many cups can you fill?

We need to divide 8/9 by 1/16. Okay, first step? Flip the second fraction. So, 1/16 becomes 16/1. Then, multiply 8/9 by 16/1. That's 128/9. That simplifies to 14 2/9. So, you can fill 14 cups and then someone gets stuck with 2/9 of a cup, which isn't great, but 14 people get full cups.

Next up, you're dishing out pizza. Unfortunately, you didn't plan this well. You only have 7/8 of a pizza on hand. You somehow only ordered one pizza and then you ate one slice while filling punch cups. There are 21 people at your party. How much of the pizza will each person get?

This is 7/8 divided by 21. Remember, 21 is the same as 21/1, so to get its reciprocal, we do 1/21. Now, we multiply 7/8 by 1/21. That's 7/168. That simplifies to 1/24. So, everyone gets 1/24 of the pizza. I call the pepperoni slice!

Let's try one more of these. After the pizza debacle, you're rationing your other snacks. You turn to your guacamole, of which you have 4/5 of a pound. You've overanalyzed this a bit and determined that people use about a tablespoon, or 1/32 of a pound, on each chip. How many chips can dip in your guacamole?

This is 4/5 divided by 1/32. Let's flip 1/32 to get 32/1. Then, multiply 4/5 by 32/1. That's 128/5, or 25 3/5. Hmmm… 25 chips. This isn't only a good lesson in dividing fractions; it's also a good lesson in party planning.

Dividing Mixed Numbers

Rather than focus on effective party preparation tips, let's take our fraction division to the next level and discuss dividing mixed numbers. To divide mixed numbers, we follow four steps. Step one: convert to improper fractions. So, if we have 3 1/3, we multiply the whole number times the denominator. That's 3 * 3, or 9. Then, add that to the numerator. So, we get 10/3.

Next, we follow the steps to divide fractions. Flip the second one, then multiply, then simplify. So, with 3 1/3 divided by 5 1/2, we convert both to improper fractions. We know 3 1/3 is 10/3. With 5 1/2, 5 * 2 is 10. Add 10 and 1 and get 11/2. Then, we flip that one to get 2/11. So, 10/3 * 2/11. 10 * 2 is 20. 11 * 3 is 33. So, 20/33. That looks like it should simplify, but it actually doesn't. So, we're done!

Practice Dividing Mixed Numbers

Let's try some in context. We're going to leave the party behind and talk about flowers. Let's say you're building a raised flower bed out of some scrap lumber. You have a board that's 10 3/4 feet long. You want pieces that are 2 1/2 feet long for the flower bed. How many pieces can you get?

We divide 10 3/4 by 2 1/2. First, convert to improper fractions. 10 3/4 becomes 43/4. 2 1/2 becomes 5/2. Next, flip 5/2 to get 2/5. Now, multiply 43/4 times 2/5. That's 86/20. That simplifies to 4 3/10. You needed four sides, so you have enough wood!

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