### Comparing fractions

In development to Fractions, us learned the fractions room a method of reflecting **part** the something. Fractions space useful, since they let us tell exactly how lot we have of something. Part fractions are larger than others. Because that 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 that 7/8 is larger. The illustration provides it straightforward to **compare** this fractions. But how could we have done it there is no the pictures?

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

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

Earlier, we saw that fractions have actually two parts.

One component is the optimal number, or** numerator**.

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

The denominator tells united state how many **parts** room in a whole.

The molecule tells us how countless of those components we have.

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

This way we deserve to **compare** this fractions simply by looking at the numerator.

Here, 5 is an ext than 4...

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

Let's watch at another example. I m sorry of these is larger: 2/8 or 6/8?

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

Both fractions have actually the exact same denominator.

So we compared the numerators. 6 is bigger than 2, for this reason 6/8 is more than 2/8.

As you saw, if 2 or an ext fractions have the same denominator, you deserve to compare them by feather at your numerators. As you deserve to see below, 3/4 is bigger than 1/4. The larger the numerator, the larger the fraction.

### Comparing fractions with various denominators

On the ahead page, we compared fractions that have actually the same **bottom numbers**, or **denominators**. However you understand that fractions can have **any** number together a denominator. What happens as soon as you should compare fountain with various bottom numbers?

For example, i beg your pardon of this is larger: 2/3 or 1/5? It's difficult to tell just by looking at them. After ~ all, 2 is bigger than 1, but the denominators aren't the same.

If you look at the picture, though, the distinction is clear: 2/3 is bigger than 1/5. V an illustration, that was basic to to compare these fractions, but how could we have actually done it there is no the picture?

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

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

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

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

Our first step is to discover numbers that deserve to be divided evenly through 8.

Using a multiplication table provides this easy. All of the number on the 8 row deserve to be split evenly through 8.

Now let's look at our second denominator: 6.

We have the right to use the multiplication table again. Every one of the numbers in the 6 row deserve to be split evenly by 6.

Let's compare the two rows. The looks favor there room a few numbers that deserve to be divided evenly through both 6 and 8.

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

Now we're walking to adjust our fractions so they both have the same denominator: 24.

To carry out that, we'll have actually to readjust the molecule the same method we adjusted the denominators.

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

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

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

5 time 3 amounts to 15. So we've changed 5/8 right into 15/24.

We deserve to do the because any kind of number over itself is equal to 1.

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

So as soon as we multiply 5/8 by 3/3...we're really multiplying 5/8 by 1.

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

Since any number times 1 is equal to itself...we deserve to say the 5/8 is same to 15/24.

Now we'll execute the same to our other fraction: 4/6. We also readjusted its denominator come 24.

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

So we'll additionally multiply the numerator by 4.

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

Now that the denominators room the same, we can compare the two fractions by looking at their numerators.

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

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

### Rjuniorg8.comcing fractions

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

If you did the math or also just looked at the picture, you might have been able to tell that they're **equal**. In various other words, 4/8 and also 1/2 mean the exact same thing, also though they're written differently.

If 4/8 way the very same thing together 1/2, why no just speak to it that? **One-half** is much easier to say 보다 **four-eighths**, and also for most world it's additionally easier to understand. After all, when you eat out through a friend, you separation the bill in **half**, no in **eighths**.

If you compose 4/8 as 1/2, you're **rjuniorg8.comcing** it. As soon as we **rjuniorg8.comce** a fraction, we're writing it in a much easier form. Rjuniorg8.comced fractions are constantly **equal** to the original fraction.

We already rjuniorg8.comced 4/8 come 1/2. If girlfriend look at the examples below, you have the right to see that various other numbers can be rjuniorg8.comced come 1/2 as well. These fractions space all **equal**.

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

These fractions have actually all been rjuniorg8.comced to a simpler type as well.

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

Click with the slideshow come learn exactly how to rjuniorg8.comce fractions by **dividing**.

Let's try rjuniorg8.comcing this fraction: 16/20.

Since the numerator and also denominator space **even numbers**, you have the right to divide lock by 2 come rjuniorg8.comce the fraction.

First, we'll division the molecule by 2. 16 separated by 2 is 8.

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

We've rjuniorg8.comced 16/20 to 8/10. We could also say that 16/20 is same to 8/10.

If the numerator and also denominator can still be divided by 2, us can proceed rjuniorg8.comcing the fraction.

8 separated by 2 is 4.

10 divided by 2 is 5.

Since there's no number that 4 and also 5 can be divided by, us can't rjuniorg8.comce 4/5 any type of further.

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

Let's shot rjuniorg8.comcing an additional fraction: 6/9.

While the molecule is even, the denominator is one **odd number**, so us can't rjuniorg8.comce by splitting by 2.

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

Let's find 6 and also 9 on the **same** **row**. As you deserve to see, 6 and 9 can both be separated by 1 and also 3.

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

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

3 is the **GCD** that 6 and 9 because it's the **largest** number they can be divided by.

So we'll divide the numerator by 3. 6 divided by 3 is 2.

Then we'll divide the denominator by 3. 9 split by 3 is 3.

Now we've rjuniorg8.comced 6/9 come 2/3, i m sorry is its simplest form. We could additionally say that 6/9 is equal to 2/3.

Irrjuniorg8.comcible fractionsNot every fractions have the right to be rjuniorg8.comced. Some are currently as simple as they have the right to be. For example, friend can't rjuniorg8.comce 1/2 due to the fact that there's no number other than 1 that both 1 and 2 have the right to be divided by. (For that reason, friend can't rjuniorg8.comce **any** portion that has actually a molecule of 1.)

Some fountain that have actually larger numbers can't it is in rjuniorg8.comced either. Because that instance, 17/36 can't be rjuniorg8.comced due to the fact that there's no number the both 17 and also 36 have the right to be divided by. If girlfriend can't find any kind of **common multiples** because that the number in a fraction, opportunities are it's **irrjuniorg8.comcible**.

Rjuniorg8.comce each fraction to its simplest form.

### Mixed numbers and improper fractions

In the ahead lesson, you learned around **mixed numbers**. A blended number has actually both a **fraction **and a **whole number**. An example is 1 2/3. You'd check out 1 2/3 choose this: **one and also two-thirds**.** **

Another way to create this would certainly be 5/3, or **five-thirds**. These 2 numbers look different, but they're in reality the same. 5/3 is one **improper fraction**. This just method the numerator is **larger** 보다 the denominator.

There space times as soon as you may prefer to use an improper fraction instead the a blended number. It's easy to readjust a blended number into an not correct fraction. Let's discover how:

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

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

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

1 times 4 equals 4.

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

4 plus 1 amounts to 5.

The denominator stays the same.

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

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

Let's convert another mixed number: 2 2/5.

First, we'll multiply the whole number through the denominator. 2 time 5 equals 10.

Next, we'll add 10 come the numerator. 10 plus 2 equals 12.

As always, the denominator will stay the same.

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

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

Converting improper fractions into mixed numbers

Improper fountain are useful for math troubles that usage fractions, together you'll discover later. However, they're likewise more difficult to read and also understand 보다 **mixed** **numbers**. Because that example, it's a lot easier to photo 2 4/7 in your head 보다 18/7.

Click with the slideshow to learn how to adjust an improper portion into a mixed number.

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

You can think the any portion as a **division** **problem**. Simply treat the line in between the numbers favor a division sign (/).

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

10 split by 4 equates to 2...

10 split by 4 amounts to 2... V a remainder that 2.

The answer, 2, will come to be our whole number due to the fact that 10 can be split by 4 **twice**.

And the **remainder**, 2, will become the numerator of the fraction because we have 2 parts left over.

The denominator continues to be the same.

So 10/4 amounts to 2 2/4.

Let's try another example: 33/3.

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

33 divided by 3...

33 separated by 3... Equates to 11, through no remainder.

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

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There is no remainder, therefore we deserve to see the our improper portion was in reality a whole number. 33/3 equals 11.