### Comparing fractions

In introduction to Fractions, us learned that fractions space a way of showing **part** the something. Fractions room useful, due to the fact that they let us tell precisely how much we have of something. Part fractions are bigger than others. For example, i m sorry is larger: 6/8 the a pizza or 7/8 the a pizza?

In this image, we have the right to see the 7/8 is larger. The illustration makes it basic to **compare** this fractions. Yet how could we have done it there is no the pictures?

Click with the slideshow to learn just how to compare fractions.

You are watching: Is 1/5 greater than 2/8

Earlier, we observed that fractions have two parts.

One part is the top number, or** numerator**.

The other is the bottom number, or **denominator**.

The denominator tells united state how countless **parts** are in a whole.

The molecule tells us how plenty of of those parts we have.

When fractions have the same denominator, it means they're separation into the same variety of parts.

This method we can **compare** these fractions just by looking at the numerator.

Here, 5 is an ext than 4...

Here, 5 is an ext than 4...so we can tell the 5/6 is an ext than 4/6.

Let's look at at an additional example. Which of these is larger: 2/8 or 6/8?

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

Both fractions have the exact same denominator.

So we compared the numerators. 6 is larger than 2, therefore 6/8 is much more than 2/8.

As you saw, if two or an ext fractions have the very same denominator, you can compare castle by feather at your numerators. Together you have the right to see below, 3/4 is larger than 1/4. The larger the numerator, the bigger the fraction.

### Comparing fractions with various denominators

On the vault page, we contrasted fractions that have the same **bottom numbers**, or **denominators**. Yet you understand that fractions can have **any** number as a denominator. What happens when you need to compare fountain with different bottom numbers?

For example, which of this is larger: 2/3 or 1/5? It's challenging to tell simply by looking at them. After all, 2 is bigger than 1, but the platform aren't the same.

If girlfriend look at the picture, though, the distinction is clear: 2/3 is bigger than 1/5. V an illustration, it was basic to compare these fractions, but how can we have actually done it without the picture?

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

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

Before us compare them, we require to adjust both fractions so they have actually the exact same **denominator**, or bottom number.

First, we'll discover the smallest number that can be separated by both denominators. We contact that the **lowest common denominator**.

Our very first step is to discover numbers that have the right to be divided evenly through 8.

Using a multiplication table renders this easy. Every one of the numbers on the 8 row can be divided evenly by 8.

Now let's look in ~ our second denominator: 6.

We have the right to use the multiplication table again. All of the numbers in the 6 row have the right to be separated evenly by 6.

Let's to compare the 2 rows. The looks choose there room a couple of numbers that have the right to be split evenly through both 6 and also 8.

24 is the the smallest number that shows up on both rows, for this reason it's the **lowest common denominator**.

Now we're going to readjust our fractions so lock both have actually the exact same denominator: 24.

To perform that, we'll have to adjust the molecule the same method we readjusted the denominators.

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

Let’s look at 5/8 again. In stimulate to change the denominator to 24...we had to main point 8 through 3.

Since we multiplied the denominator through 3, we'll likewise multiply the numerator, or peak number, by 3.

5 times 3 equals 15. So we've adjusted 5/8 right into 15/24.

We can do the because any number end itself is equal to 1.

So as soon as we multiply 5/8 by 3/3...

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

Since any number times 1 is same to itself...

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

Now we'll perform the exact same to our other fraction: 4/6. We also changed its denominator to 24.

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

So we'll additionally multiply the numerator by 4.

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

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

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

16/24 is bigger than 15/24... So 4/6 is bigger than 5/8.

### Rgaianation.netcing fractions

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

If girlfriend did the mathematics or even just looked at the picture, you can have to be able come tell the they're **equal**. In various other words, 4/8 and also 1/2 average the same thing, also though they're created differently.

If 4/8 method the same thing as 1/2, why no just contact it that? **One-half** is much easier to say 보다 **four-eighths**, and for most civilization it's likewise easier come understand. After ~ all, when you eat out v a friend, you break-up the invoice in **half**, no in **eighths**.

If you write 4/8 as 1/2, you're **rgaianation.netcing** it. When we **rgaianation.netce** a fraction, we're writing it in a simpler form. Lessened fractions are always **equal** to the initial fraction.

We currently rgaianation.netced 4/8 come 1/2. If girlfriend look in ~ the instances below, you deserve to see that other numbers can be rgaianation.netced to 1/2 as well. This fractions are all **equal**.

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

These fractions have actually all been lessened to a simpler form as well.

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

Click v the slideshow come learn how to mitigate fractions through **dividing**.

Let's try rgaianation.netcing this fraction: 16/20.

Since the numerator and also denominator space **even numbers**, you have the right to divide lock by 2 to alleviate the fraction.

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

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

We've diminished 16/20 come 8/10. We could likewise say the 16/20 is equal to 8/10.

If the numerator and denominator have the right to still be split by 2, us can proceed rgaianation.netcing the fraction.

8 separated by 2 is 4.

10 split by 2 is 5.

Since there's no number that 4 and 5 can be separated by, us can't mitigate 4/5 any kind of further.

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

Let's try rgaianation.netcing another fraction: 6/9.

While the molecule is even, the denominator is an **odd number**, so we can't minimize by splitting by 2.

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

Let's find 6 and also 9 top top the **same** **row**. Together you have the right to see, 6 and 9 can both be separated by 1 and 3.

Dividing by 1 won't adjust these fractions, for this reason we'll usage the **largest** number the 6 and also 9 can be split by.

That's 3. This is called the **greatest typical divisor**, or **GCD**. (You can likewise call it the **greatest usual factor**, or **GCF**.)

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

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

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

Now we've diminished 6/9 to 2/3, i beg your pardon is its easiest form. We could likewise say the 6/9 is equal to 2/3.

Irrgaianation.netcible fractionsNot all fractions deserve to be rgaianation.netced. Some are currently as simple as they can be. Because that example, you can't minimize 1/2 due to the fact that there's no number various other than 1 the both 1 and 2 have the right to be separated by. (For the reason, friend can't alleviate **any** fraction that has a numerator of 1.)

Some fractions that have larger number can't be decreased either. For instance, 17/36 can't be rgaianation.netced since there's no number the both 17 and 36 have the right to be split by. If you can't find any kind of **common multiples** for the number in a fraction, possibilities are it's **irrgaianation.netcible**.

Rgaianation.netce each portion to its most basic form.

### Mixed numbers and improper fractions

In the ahead lesson, friend learned about **mixed numbers**. A combined number has both a **fraction **and a **whole number**. An instance is 1 2/3. You'd check out 1 2/3 choose this: **one and two-thirds**.** **

Another method to write this would certainly be 5/3, or **five-thirds**. These 2 numbers watch different, but they're in reality the same. 5/3 is an **improper fraction**. This just means the molecule is **larger** 보다 the denominator.

There are times when you may prefer to use an improper portion instead the a mixed number. It's simple to change a blended number into an wrong fraction. Let's learn how:

Let's transform 1 1/4 right into an improper fraction.

First, we'll require to uncover out how plenty of **parts** comprise the totality number: 1 in this example.

To carry out this, we'll multiply the **whole number**, 1, by the denominator, 4.

1 times 4 amounts to 4.

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

4 plus 1 equals 5.

The denominator stays the same.

Our improper portion is 5/4, or five-fourths. So we might say the 1 1/4 is equal to 5/4.

This way there are **five** 1/4s in 1 1/4.

Let's convert an additional mixed number: 2 2/5.

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

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

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

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

Try This!Try convert these blended numbers right into improper fractions.

Converting not correct fractions into mixed numbers

Improper fountain are useful for math troubles that usage fractions, as you'll learn later. However, they're also more an overwhelming to read and also understand 보다 **mixed** **numbers**. For example, it's a lot easier to picture 2 4/7 in your head 보다 18/7.

Click v the slideshow come learn how to change an improper portion into a combined number.

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

You can think that any fraction as a **division** **problem**. Simply treat the line in between the numbers like a department sign (/).

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

10 split by 4 equals 2...

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

The answer, 2, will end up being our entirety number since 10 deserve to be divided by 4 **twice**.

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

The denominator remains the same.

So 10/4 equates to 2 2/4.

Let's try another example: 33/3.

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

33 split by 3...

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

The answer, 11, will come to be our totality number.

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There is no remainder, therefore we can see the our improper fraction was actually a totality number. 33/3 amounts to 11.