Comparing fractions

In arrival to Fractions, us learned the fractions room a means of reflecting part the something. Fractions space useful, since they let us tell exactly how lot we have actually of something. Part fractions are larger than others. For example, i m sorry is larger: 6/8 of a pizza or 7/8 the a pizza?


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In this image, we can see the 7/8 is larger. The illustration renders it simple to compare this fractions. Yet how might we have actually done it without the pictures?

Click through the slideshow to learn exactly how to compare fractions.

You are watching: Is 2/8 greater than 2/4

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Earlier, we experienced that fractions have two parts.

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One part is the optimal number, or numerator.

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The other is the bottom number, or denominator.

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The denominator tells us how numerous parts room in a whole.

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The numerator tells us how plenty of of those components we have.

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When fractions have the very same denominator, it means they're split into the same number of parts.

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This means we deserve to compare these fractions simply by looking at the numerator.

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Here, 5 is more than 4...

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Here, 5 is more than 4...so we deserve to tell that 5/6 is more than 4/6.

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Let's look at another example. I beg your pardon of this is larger: 2/8 or 6/8?

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If you assumed 6/8 was larger, you to be right!

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Both fractions have the same denominator.

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So we compared the numerators. 6 is bigger than 2, so 6/8 is more than 2/8.

As friend saw, if two or much more fractions have actually the exact same denominator, you can compare lock by spring at your numerators. As you deserve to see below, 3/4 is larger than 1/4. The larger the numerator, the larger the fraction.


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Comparing fractions with various denominators

On the previous page, we contrasted fractions that have actually the very same bottom numbers, or denominators. However you recognize that fractions can have any number together a denominator. What happens once you need to compare fractions with various bottom numbers?

For example, i m sorry of these is larger: 2/3 or 1/5? It's complicated to tell simply by looking at them. After ~ all, 2 is bigger than 1, but the denominators aren't the same.


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If girlfriend look at the picture, though, the distinction is clear: 2/3 is larger than 1/5. V an illustration, that was straightforward to compare these fractions, yet how could we have done it without the picture?

Click v the slideshow come learn just how to to compare fractions with various denominators.

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Let's compare these fractions: 5/8 and also 4/6.

Before we compare them, we need to adjust both fractions so they have the same denominator, or bottom number.

First, we'll uncover the the smallest number that deserve to be divided by both denominators. We contact that the lowest typical denominator.

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Our an initial step is to uncover numbers that deserve to be divided evenly by 8.

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Using a multiplication table renders this easy. All of the number on the 8 row can be split evenly by 8.

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Now let's look at our 2nd denominator: 6.

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We deserve to use the multiplication table again. Every one of the numbers in the 6 row deserve to be separated evenly through 6.

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Let's compare the two rows. That looks favor there space a few numbers that can be separated evenly by both 6 and also 8.

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24 is the the smallest number that appears on both rows, for this reason it's the lowest typical denominator.

Now we're going to adjust our fountain so castle both have the exact same denominator: 24.

To do that, we'll have to change the molecule the same means we readjusted the denominators.

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Let’s look at 5/8 again. In bespeak to readjust the denominator to 24...

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Let’s look in ~ 5/8 again. In bespeak to readjust the denominator to 24...we had actually to multiply 8 by 3.

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Since us multiplied the denominator by 3, we'll also multiply the numerator, or height number, by 3.

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5 times 3 amounts to 15. For this reason we've adjusted 5/8 into 15/24.

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We have the right to do that because any kind of number end itself is same to 1.

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So once we main point 5/8 through 3/3...

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So when we main point 5/8 by 3/3...we're yes, really multiplying 5/8 through 1.

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Since any kind of number times 1 is equal to itself...

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Since any number time 1 is same to itself...we deserve to say that 5/8 is same to 15/24.

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Now we'll carry out the same to our various other fraction: 4/6. Us also changed its denominator to 24.

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Our old denominator was 6. To obtain 24, we multiplied 6 by 4.

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So we'll likewise multiply the molecule by 4.

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4 times 4 is 16. Therefore 4/6 is equal to 16/24.

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Now the the denominators space the same, we have the right to compare the 2 fractions by spring at your numerators.

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16/24 is larger than 15/24...

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16/24 is bigger than 15/24... For this reason 4/6 is bigger than 5/8.

Rbetterworld2016.orgcing fractions

Which of these is larger: 4/8 or 1/2?


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If friend did the math or also just looked at the picture, you could have been able to tell the they're equal. In various other words, 4/8 and also 1/2 median the same thing, even though they're composed differently.

If 4/8 way the exact same thing as 1/2, why no just contact it that? One-half is simpler to say than four-eighths, and for most world it's also easier to understand. After ~ all, as soon as you eat out through a friend, you split the bill in half, no in eighths.

If you create 4/8 together 1/2, you're rbetterworld2016.orgcing it. Once we rbetterworld2016.orgce a fraction, we're creating it in a much easier form. Decreased fractions are constantly equal to the original fraction.

We currently rbetterworld2016.orgced 4/8 to 1/2. If you look at the instances below, you deserve to see that other numbers can be rbetterworld2016.orgced to 1/2 as well. These fractions are all equal.

5/10 = 1/211/22 = 1/236/72 = 1/2

These fractions have all been rbetterworld2016.orgced to a simpler form as well.

4/12 = 1/314/21 = 2/335/50 = 7/10

Click through the slideshow to learn exactly how to rbetterworld2016.orgce fractions by dividing.

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Let's shot rbetterworld2016.orgcing this fraction: 16/20.

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Since the numerator and denominator are even numbers, you can divide castle by 2 to alleviate the fraction.

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First, we'll division the numerator by 2. 16 divided by 2 is 8.

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Next, we'll divide the denominator through 2. 20 split by 2 is 10.

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We've lessened 16/20 to 8/10. We could additionally say that 16/20 is equal to 8/10.

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If the numerator and denominator can still be split by 2, us can continue rbetterworld2016.orgcing the fraction.

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8 split by 2 is 4.

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10 divided by 2 is 5.

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Since there's no number that 4 and also 5 deserve to be separated by, we can't minimize 4/5 any kind of further.

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This way 4/5 is the simplest form of 16/20.

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Let's shot rbetterworld2016.orgcing another fraction: 6/9.

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While the numerator is even, the denominator is one odd number, so we can't rbetterworld2016.orgce by splitting by 2.

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Instead, we'll require to uncover a number the 6 and also 9 deserve to be split by. A multiplication table will make that number straightforward to find.

Let's uncover 6 and also 9 on the same row. As you can see, 6 and also 9 can both be divided by 1 and also 3.

Dividing by 1 won't adjust these fractions, so we'll usage the largest number that 6 and 9 have the right to be separated by.

That's 3. This is dubbed the greatest usual divisor, or GCD. (You can also call the the greatest typical factor, or GCF.)

3 is the GCD that 6 and 9 since it's the largest number they have the right to be divided by.

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So we'll division the numerator by 3. 6 separated by 3 is 2.

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Then we'll division the denominator by 3. 9 divided by 3 is 3.

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Now we've decreased 6/9 come 2/3, i m sorry is its easiest form. We could additionally say that 6/9 is same to 2/3.

Irrbetterworld2016.orgcible fractions

Not every fractions have the right to be rbetterworld2016.orgced. Part are currently as simple as they can be. For example, you can't mitigate 1/2 due to the fact that there's no number other than 1 the both 1 and 2 deserve to be divided by. (For that reason, you can't rbetterworld2016.orgce any fraction that has a numerator of 1.)

Some fractions that have larger number can't be diminished either. Because that instance, 17/36 can't be rbetterworld2016.orgced because there's no number that both 17 and 36 can be separated by. If friend can't find any common multiples for the numbers in a fraction, opportunities are it's irrbetterworld2016.orgcible.

Try This!

Rbetterworld2016.orgce each portion to its most basic form.


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Mixed numbers and improper fractions

In the previous lesson, girlfriend learned around mixed numbers. A blended number has both a fraction and a whole number. An example is 1 2/3. You'd review 1 2/3 favor this: one and also two-thirds.

Another way to compose this would be 5/3, or five-thirds. These 2 numbers look different, but they're actually the same. 5/3 is one improper fraction. This just means the molecule is larger than the denominator.

There room times once you might prefer to use an improper portion instead the a combined number. It's easy to change a mixed number right into an wrong fraction. Let's learn how:

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Let's transform 1 1/4 right into an not correct fraction.

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First, we'll need to discover out how countless parts comprise the entirety number: 1 in this example.

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To perform this, we'll main point the whole number, 1, by the denominator, 4.

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1 times 4 equates to 4.

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Now, let's add that number, 4, to the numerator, 1.

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4 add to 1 equates to 5.

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The denominator continues to be the same.

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Our improper fraction is 5/4, or five-fourths. For this reason we might say the 1 1/4 is equal to 5/4.

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This means there are five 1/4s in 1 1/4.

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Let's convert one more mixed number: 2 2/5.

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First, we'll main point the whole number by the denominator. 2 times 5 equates to 10.

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Next, we'll include 10 to the numerator. 10 add to 2 amounts to 12.

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As always, the denominator will continue to be the same.

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So 2 2/5 is same to 12/5.

Try This!

Try convert these blended numbers right into improper fractions.


Converting improper fractions right into mixed numbers

Improper fractions are useful for math problems that use fractions, together you'll learn later. However, they're additionally more challenging to read and also understand than mixed numbers. Because that example, it's a lot much easier to photo 2 4/7 in her head than 18/7.

Click through the slideshow to learn how to adjust an improper portion into a blended number.

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Let's revolve 10/4 into a mixed number.

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You have the right to think that any fraction as a division problem. Just treat the line between the numbers choose a department sign (/).

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So we'll divide the numerator, 10, by the denominator, 4.

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10 split by 4 equates to 2...

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10 divided by 4 amounts to 2... With a remainder the 2.

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The answer, 2, will come to be our whole number because 10 deserve to be separated by 4 twice.

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And the remainder, 2, will end up being the numerator of the portion because we have actually 2 parts left over.

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The denominator stays the same.

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So 10/4 equals 2 2/4.

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Let's shot another example: 33/3.

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We'll division the numerator, 33, by the denominator, 3.

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33 separated by 3...

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33 divided by 3... Equates to 11, with no remainder.

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The answer, 11, will end up being our totality number.

See more: Is Shipley'S Open On Christmas, Holiday Fun, Donut Box, &Raquo Blog Archive

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There is no remainder, for this reason we have the right to see that our improper portion was in reality a totality number. 33/3 equates to 11.