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  • Hi there! Welcome to Math Antics. In this video we are going to learn how to compare fractions.

  • Hmmmthis fraction has 25% more fiber than this fraction

  • Oooo! But this fraction has trisodium phosphate!

  • Wellit’s not quite like that.

  • Comparing fractions just means telling which one is bigger.

  • You know, just like we do with regular numbers when we use the greater-than, less-than, and equal-to signs.

  • That sounds easy, right? But unfortunately, unlike regular numbers,

  • it’s not always easy to tell which fraction is bigger just by looking at them.

  • That’s because the value of a fraction depends on both the top AND bottom numbers and how they relate to each other.

  • For example, if you have to compare these two fractions, 1 over 3 and 1 over 10,

  • some of you might be tempted to say that 1 over 10 is bigger because you know that 10 is bigger than 3, right?

  • But we need to remember that the fraction is really a number written like a division problem,

  • and its value depends on that division.

  • So in this case, the 1 over 3 is really the bigger fraction

  • because its decimal value (what you get when you divide) is 0.333 but the value of 1 over 10 is only 0.1

  • Okay, so comparing fractions isn’t quite as easy as comparing regular numbers,

  • but that doesn’t mean it’s going to be that hard.

  • Were going to learn two methods for comparing fractions that make it very easy.

  • The first method is called cross-multiplying,

  • and it takes advantage of the fact that it’s easy to compare fractions with the same bottom numbers.

  • If two fractions have the same bottom numbers, then we can just compare the top numbers.

  • That’s because we are comparing the same size parts.

  • Were comparing fourths to fourths, eighths to eighths, tenths to tenths, and so on

  • And the top number just tells us how many of those parts we have,

  • so it’s easy to see that 5 eighths is more than 3 eighths.

  • But many times, youll have to compare fractions that have different bottom numbers. (or different size parts)

  • Fortunately, there’s a trick we can do to make the comparison easy.

  • In the Math Antics Videos about Common Denominators,

  • we learn a simple method for changingunlike fractions” (with different bottom numbers)

  • intolike fractions” (with the same bottom number).

  • Basically, it shows how you can multiply two unlike fractions

  • by wholes fractions made from the different bottom numbers,

  • so you end up with the same bottom number.

  • This will give you two newequivalentfractions that you can easily add, subtract, or compare.

  • But, there’s a shortcut for comparing fractions.

  • As long as we know that the bottom numbers of our fractions are the same,

  • we don’t really need to know what that number is.

  • We just need to know what the top numbers will be, since those are the ones that well actually compare.

  • So instead of multiplying each fraction by a whole fraction,

  • we can just multiply the top number of each fraction by the bottom number of the other fraction.

  • This is calledCross Multiplyingbecause if you draw a diagram of what youre multiplying,

  • it forms a criss-cross pattern.

  • After you cross multiply, you will have two numbers that would be the new top numbers

  • if you had madelikefractions, and those numbers will show you which fraction is greater.

  • Let’s try this cross-multiplying method on an example or two.

  • Let’s compare the fractions: 7 over 8 and 4 over 5.

  • We start by multiplying the second fraction’s bottom number (5) by the first fraction’s top number (7)

  • and that gives us 35 for the new top number on this side.

  • Youll always keep the answer on the side of the top number that you multiplied.

  • now for the other side.

  • The bottom number (8) times the top number (4) gives us 32 for its new top number.

  • Ah-ha! Now it’s easy to see that the fraction 7 over 8 is greater than the fraction 4 over 5

  • because its new top number (35) is greater than the other new top number (32).

  • Let’s do one more comparison by cross multiplying.

  • Let’s compare 6 over 11 to 9 over 15.

  • First well multiply 15 by 6 to get the new top number of the first side, which is 90.

  • Now you can use a calculator to do the multiplications if you need to.

  • Next, we multiply 11 by 9 to get the second new top number, which is 99.

  • So, that tells us that the second fraction (9 over 15) is greater than the first fraction because its new top number (99) is bigger.

  • Pretty simple, huh?

  • Okay, cross multiplying is pretty cool,

  • but there’s another way to compare fractions that you need to know about.

  • But this one is only really good if you can use a calculator.

  • Remember, the reason that fractions are tricky to compare is because theyre really division problems.

  • But if we want to, we can just do the division and get the answer,

  • which is the decimal value of the fraction.

  • So if you have two fractions to compare, you can just do the division

  • (preferably using a calculator) and then compare the decimal values.

  • For example, let’s say I offered to give you either 5/12 of a pizza or 7/15 of a pizza.

  • Now, you happen to be really hungry, so you want to choose the biggest amount,

  • but it’s not very easy to tell just by looking which is bigger: 5/12 or 7/15

  • This is were decimal values can really help you out.

  • If you convert the fractions to decimals by doing division,

  • it will make it much easier to see which one is bigger.

  • 5 divided by 12 is about 0.42

  • and 7 divided by 15 is about 0.47

  • Yep, that makes comparing them much easier.

  • Since 0.47 is greater than 0.42, it means that 7/15 is greater than 5/12.

  • And that means that you’d rather have 7/15 of the pizza!

  • Sometimes when you compare fractions this way,

  • youll find two fractions that look different, but have the same decimal value: like 3/8 and 15/40.

  • If you convert each fraction to a decimal, youll see that they both have the value 0.375

  • Two fractions that have different top and bottom numbers, but the same value are calledequivalent fractions’.

  • If two fractions are equivalent, then you can just use the equal sign to show the comparison between them, like this

  • Alright, so those are two great methods you can use to compare fractions.

  • Cross multiplying is simple and works great, even if you don’t have a calculator.

  • And comparing the decimal vales by dividing is easy if you do have a calculator.

  • As always, practice makes perfect,

  • so spend some time doing the exercises for this section, and I’ll see you next time.

  • Learn more at www.mathantics.com

Hi there! Welcome to Math Antics. In this video we are going to learn how to compare fractions.

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B1 中級

数学のアンチティクス - 分数の比較 (Math Antics - Comparing Fractions)

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    Yassion Liu に公開 2021 年 01 月 14 日
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