### Comparing fractions

In development to Fractions, us learned that fractions are a method of mirroring **part** the something. Fractions are useful, because they let us tell exactly how much we have actually of something. Some fractions are larger than others. Because that example, i beg your pardon is larger: 6/8 that a pizza or 7/8 that a pizza?

In this image, we deserve to see that 7/8 is larger. The illustration provides it easy to **compare** these fractions. Yet how might we have done it there is no the pictures?

Click v the slideshow to learn how to compare fractions.

You are watching: Which number is bigger -2 or -4

Earlier, we observed that fractions have actually two parts.

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

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

The denominator tells us how numerous **parts** space in a whole.

The molecule tells united state how numerous of those components we have.

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

This method we deserve to **compare** these fractions simply by looking in ~ the numerator.

Here, 5 is an ext than 4...

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

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

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

Both fractions have actually the exact same denominator.

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

As friend saw, if 2 or much more fractions have the same denominator, you have the right to compare castle by looking at your numerators. As you have the right to see below, 3/4 is bigger than 1/4. The bigger the numerator, the bigger the fraction.

### Comparing fountain with different denominators

On the vault page, we contrasted fractions that have the same **bottom numbers**, or **denominators**. Yet you recognize that fractions have the right to have **any** number as a denominator. What happens when you must compare fractions with various bottom numbers?

For example, which of this is larger: 2/3 or 1/5? It's complicated to tell just by looking in ~ them. ~ all, 2 is larger than 1, but the platform aren't the same.

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

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

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

Before us compare them, we require to readjust both fountain so they have the same **denominator**, or bottom number.

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

Our first step is to discover numbers that deserve to be split evenly by 8.

Using a multiplication table provides this easy. All of the numbers on the 8 row deserve to be divided evenly by 8.

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

We can use the multiplication table again. All of the numbers in the 6 row can be split evenly by 6.

Let's to compare the two rows. That looks choose there space a couple of numbers that have the right to be divided evenly by both 6 and 8.

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

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

To execute that, we'll have to adjust the numerators the same method we readjusted the denominators.

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

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

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

5 time 3 equates to 15. For this reason we've changed 5/8 into 15/24.

We can do the because any number over itself is same to 1.

So when we multiply 5/8 by 3/3...

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

Since any number time 1 is equal to itself...

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

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

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

So we'll likewise multiply the numerator by 4.

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

Now that the denominators room the same, we have the right to compare the two fractions by feather at your numerators.

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

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

### Rdearteassociazione.orgcing fractions

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

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

If 4/8 way the exact same thing together 1/2, why not just contact it that? **One-half** is simpler to say than **four-eighths**, and for most civilization it's additionally easier come understand. After all, when you eat out through a friend, you split the bill in **half**, not in **eighths**.

If you create 4/8 as 1/2, you're **rdearteassociazione.orgcing** it. Once we **rdearteassociazione.orgce** a fraction, we're creating it in a simpler form. Rdearteassociazione.orgced fountain are constantly **equal** to the original fraction.

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

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

These fractions have all been rdearteassociazione.orgced come a simpler type as well.

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

Click with the slideshow to learn just how to rdearteassociazione.orgce fountain by **dividing**.

Let's try rdearteassociazione.orgcing this fraction: 16/20.

Since the numerator and denominator room **even numbers**, you deserve to divide lock by 2 to rdearteassociazione.orgce the fraction.

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

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

We've rdearteassociazione.orgced 16/20 to 8/10. We could likewise say that 16/20 is same to 8/10.

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

8 separated by 2 is 4.

10 divided by 2 is 5.

Since there's no number that 4 and 5 deserve to be divided by, we can't rdearteassociazione.orgce 4/5 any further.

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

Let's shot rdearteassociazione.orgcing an additional fraction: 6/9.

While the molecule is even, the denominator is one **odd number**, so we can't rdearteassociazione.orgce by splitting by 2.

Instead, we'll need to find a number that 6 and also 9 have the right to be separated by. A multiplication table will make that number simple to find.

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

Dividing by 1 won't change these fractions, therefore we'll usage the **largest** number the 6 and also 9 have the right to be split by.

That's 3. This is referred to as the **greatest typical divisor**, or **GCD**. (You can additionally call it the **greatest typical factor**, or **GCF**.)

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

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

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

Now we've rdearteassociazione.orgced 6/9 come 2/3, i beg your pardon is its simplest form. Us could also say the 6/9 is equal to 2/3.

Irrdearteassociazione.orgcible fractionsNot every fractions deserve to be rdearteassociazione.orgced. Some are already as basic as they can be. For example, friend can't rdearteassociazione.orgce 1/2 since there's no number various other than 1 that both 1 and also 2 deserve to be separated by. (For that reason, girlfriend can't rdearteassociazione.orgce **any** fraction that has actually a numerator of 1.)

Some fractions that have actually larger numbers can't be rdearteassociazione.orgced either. For instance, 17/36 can't be rdearteassociazione.orgced due to the fact that there's no number the both 17 and 36 can be split by. If friend can't find any kind of **common multiples** for the number in a fraction, opportunities are it's **irrdearteassociazione.orgcible**.

Rdearteassociazione.orgce each fraction to its easiest form.

### Mixed numbers and also improper fractions

In the previous lesson, girlfriend learned about **mixed numbers**. A combined 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 two-thirds**.** **

Another method to write this would be 5/3, or **five-thirds**. These two numbers look different, yet they're actually the same. 5/3 is one **improper fraction**. This just way the molecule is **larger** 보다 the denominator.

There are times when you may prefer to use an improper fraction instead of a mixed number. It's basic to change a blended number into an improper fraction. Let's find out how:

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

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

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

1 time 4 amounts to 4.

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

4 add to 1 amounts to 5.

The denominator remains the same.

Our improper fraction is 5/4, or five-fourths. So we might say that 1 1/4 is same 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 by the denominator. 2 time 5 amounts to 10.

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

As always, the denominator will stay the same.

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

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

Converting not correct fractions into mixed numbers

Improper fountain are helpful for math problems that use fractions, as you'll find out later. However, they're additionally more complicated to read and also understand than **mixed** **numbers**. Because that example, it's a lot less complicated to snapshot 2 4/7 in your head than 18/7.

Click v the slideshow come learn just how to adjust an improper fraction into a mixed number.

Let's revolve 10/4 right into a combined number.

You deserve to think that any portion as a **division** **problem**. Simply treat the line in between the numbers prefer a department sign (/).

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

10 separated by 4 equals 2...

10 split by 4 equates to 2... With a remainder the 2.

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

And the **remainder**, 2, will come to be the molecule of the portion because we have 2 parts left over.

The denominator stays the same.

So 10/4 equates to 2 2/4.

Let's shot another example: 33/3.

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

33 divided by 3...

33 divided by 3... Equals 11, through no remainder.

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

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There is no remainder, for this reason we can see that our improper fraction was in reality a totality number. 33/3 amounts to 11.