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  • Youve probably noticed that weve been talking an awful lot about fractions around here lately.

  • Well, now I’m going to tell you something you can do with fractions that’s really easy.

  • No, nonot juggling fractions.

  • [circus music]

  • Although that is pretty easyfor me.

  • I’m talking about something even easier than that.

  • I’m talking about multiplying fractions.

  • Multiplying fractions is super easy. In fact it’s easier than adding fractions,

  • and that’s why were going to learn it first.

  • The reason it’s easier is because fractions are really just division problems.

  • And multiplication and division get along much better than addition and division.

  • Now since fractions are division, that means if I have the problem one-fourth times two-thirds,

  • it’s the same as the problem: 1 divided by 4 times 2 divided by 3.

  • That means I’ve got both multiplication and division in the same problem.

  • And because they get along so well, that means I can just rearrange our problem to look like this.

  • Now it looks like two multiplication problems that are being divided.

  • Andit looks just like a fraction.

  • In fact, if we go ahead and do the multiplications

  • 1 times 2 equals 2

  • and 4 times 3 equals 12

  • Then we do have a fraction, and it’s the answer to our problem.

  • So, what does this all mean?

  • Well, it means that to multiply fractions, all you have to do is multiply the top numbers,

  • and then multiply the bottom numbers, and Tada!… There’s your answer!

  • As always, let’s see an example or two.

  • Let’s try this problem: two-thirds times four-fifths

  • Now we could re-write the problem like we just saw,

  • but that’s not necessary as long as we remember the procedure.

  • First, we know our answer is going to be a fraction,

  • so let’s go ahead and write a new fraction line for it.

  • Next, we multiply the top numbers: 2 × 4 = 8

  • So 8 is the top number of our answer.

  • Last, we multiply the bottom numbers: 3 × 5 = 15

  • So 15 is the bottom number of our answer.

  • There we have it: 2/3 times 4/5 equals 8/15

  • See how easy that was? …and FUN too!

  • even funner than video games!!

  • [coo-coo clock sound]

  • Okaytime for another example.

  • Let’s try 6/11 times 7/8

  • From our multiplication table, we know that 6 × 7 = 42,

  • so 42 is the top number of our answer.

  • And on the bottom, we have 11 times 8 which is 88.

  • So, 6/11 times 7/8 equals 42/88

  • Oh, now some of you might see that this answer could be simplified,

  • but well save simplifying fractions for another video.

  • Alright, let’s see one last example. Here it is:

  • 1/2 times 4/3 times 3/5

  • Wait a minute! This has three fractions multiplied together, and that middle one looks

  • like animproperfraction cuz its top number is bigger than its bottom number.

  • Does our procedure work for this problem too?

  • Yep! All we have to do is multiply all the top numbers together

  • and then multiply all the bottom numbers together and well have our answer.

  • And this will work no matter how many fractions we have to multiply.

  • So, on the top we have: 1 time 4 is 4 …and 4 time 3 is 12.

  • And on the bottom: 2 times 3 is 6 …and 6 times 5 is 30.

  • That means our answer is 12 over 30

  • So, there you have itMultiplying fractions is easy because fractions are just another way of writing division problems.

  • But, remember, there’s another way to think about fractions.

  • We can also use fractions to represent parts of things like half of a pizza for instance.

  • But does it make sense to multiply half a pizza by another half? Actually, it does!

  • If you are thinking of fractions asparts of somethingthem multiplying fractions is really like taking part of another part.

  • For example, here’s half of a pizza.

  • You can see that if I take one-half of that half, then I get one-fourth of a pizza.

  • And if we do the multiplication: 1/2 times 1/2, you see that we DO get 1/4.

  • So that’s why you can think of multiplying fractions as taking part of another part.

  • In fact, sometimes, especially in word or story problems,

  • youll see multiplying fractions written using the wordofinstead oftimes”.

  • They may ask, “What’s three-fourths OF two-thirds?”

  • And now youll know they just mean, “What’s three-fourths TIMES two-thirds?”

  • So, whether you think of fractions as parts of something or as division problems,

  • the procedure for doing the multiplication is exactly the same!

  • Let’s do a quick review of what weve learned.

  • Multiplying fractions is even easier than adding fractions.

  • It’s easy becauseOrder of Operationssays that we can do the multiplication before the division.

  • The procedure for multiplying fractions is to multiply the top numbers to get the answer’s top number, and multiply the bottom numbers to get the answer’s bottom number.

  • If you think of fractions as parts of something, then multiplying a fraction by another fraction is the same as taking a part of a part.

  • And sometimes, especially in word problems, you might see the wordofinstead of the wordtimes”.

  • Even though multiplying fractions is so easy, it’s a good idea to practice.

  • So be sure to do the exercises, and I’ll see ya next time.

  • Learn more at www.mathantics.com

Youve probably noticed that weve been talking an awful lot about fractions around here lately.

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B1 中級 美國腔

數學反常--分數乘法法則 (Math Antics - Multiplying Fractions)

  • 18 6
    Yassion Liu 發佈於 2021 年 01 月 14 日
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