Comparing fractions

In advent to Fractions, us learned the fractions are a means of reflecting part that something. Fractions room useful, since 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 of a pizza or 7/8 that a pizza?


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In this image, we have the right to see the 7/8 is larger. The illustration provides it straightforward to compare this fractions. However how can we have actually done it without the pictures?

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

You are watching: Is 1/2 bigger than 3/4

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Earlier, we observed that fractions have two parts.

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One part is the top number, or numerator.

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The other is the bottom number, or denominator.

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The denominator tells us how countless parts are in a whole.

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

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

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This method we can compare this fractions just by looking in ~ the numerator.

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Here, 5 is more than 4...

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Here, 5 is more than 4...so we can tell that 5/6 is much more than 4/6.

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Let's look at at one more example. I m sorry of this is larger: 2/8 or 6/8?

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

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Both fractions have the exact same denominator.

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So we compared the numerators. 6 is larger than 2, therefore 6/8 is an ext than 2/8.

As girlfriend saw, if two or much more fractions have the very same denominator, you can compare lock by looking at their numerators. Together you can see below, 3/4 is bigger than 1/4. The larger the numerator, the bigger the fraction.


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Comparing fractions with various denominators

On the vault page, we contrasted fractions that have actually the same bottom numbers, or denominators. But you know that fractions have the right to have any number as a denominator. What happens as soon as you must compare fractions with different bottom numbers?

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


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If friend look at the picture, though, the distinction is clear: 2/3 is larger than 1/5. With an illustration, that was straightforward to to compare these fractions, yet how might we have actually done it there is no the picture?

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

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

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

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

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Our very first step is to uncover numbers that can be separated evenly by 8.

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Using a multiplication table makes this easy. Every one of the number on the 8 row deserve to be divided evenly by 8.

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

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We can use the multiplication table again. Every one of the number in the 6 row deserve to be separated evenly by 6.

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Let's compare the 2 rows. That looks prefer there are a couple of numbers that have the right to be separated evenly by both 6 and 8.

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

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

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

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

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

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

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

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

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

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

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

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

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Now we'll carry out the exact same to our other fraction: 4/6. We also adjusted its denominator come 24.

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

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So we'll also multiply the molecule by 4.

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4 times 4 is 16. For this reason 4/6 is same to 16/24.

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

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16/24 is bigger than 15/24...

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

Rjajalger2018.orgcing fractions

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


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

If 4/8 method the same thing together 1/2, why not just call it that? One-half is much easier to say than four-eighths, and for most civilization it's also easier come understand. After ~ all, once you eat out with a friend, you split the invoice in half, no in eighths.

If you write 4/8 together 1/2, you're rjajalger2018.orgcing it. As soon as we rjajalger2018.orgce a fraction, we're creating it in a less complicated form. Rjajalger2018.orgced fractions are always equal come the original fraction.

We already rjajalger2018.orgced 4/8 to 1/2. If you look at the instances below, you have the right to see that various other numbers can be lessened to 1/2 together well. This fractions are all equal.

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

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

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

Click with the slideshow to learn just how to mitigate fractions by dividing.

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Let's shot rjajalger2018.orgcing this fraction: 16/20.

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Since the numerator and denominator are even numbers, you have the right to divide lock by 2 to minimize the fraction.

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

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

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We've rjajalger2018.orgced 16/20 to 8/10. We could likewise say the 16/20 is equal to 8/10.

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If the numerator and denominator have the right to still be split by 2, we can proceed rjajalger2018.orgcing the fraction.

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8 separated by 2 is 4.

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10 separated 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 alleviate 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 rjajalger2018.orgcing one more fraction: 6/9.

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While the numerator is even, the denominator is one odd number, so we can't mitigate by separating by 2.

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

Let's discover 6 and 9 ~ above the same row. As you deserve to see, 6 and also 9 deserve to 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 also 9 can be separated by.

That's 3. This is referred to as the greatest common divisor, or GCD. (You can also call the the greatest usual factor, or GCF.)

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

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

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

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Now we've lessened 6/9 to 2/3, which is its simplest form. Us could also say that 6/9 is same to 2/3.

Irrjajalger2018.orgcible fractions

Not all fractions can be rjajalger2018.orgced. Some are already as basic as they can be. For example, you can't alleviate 1/2 due to the fact that there's no number other than 1 that both 1 and 2 deserve to be divided by. (For the reason, you can't rjajalger2018.orgce any portion that has a numerator of 1.)

Some fractions that have actually larger numbers can't be decreased either. Because that instance, 17/36 can't be rjajalger2018.orgced since there's no number that both 17 and also 36 can be split by. If you can't find any kind of common multiples for the numbers in a fraction, opportunities are it's irrjajalger2018.orgcible.

Try This!

Rjajalger2018.orgce each fraction to its most basic form.


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Mixed numbers and improper fractions

In the ahead lesson, you learned about mixed numbers. A mixed number has both a fraction and a whole number. An example is 1 2/3. You'd read 1 2/3 favor this: one and also two-thirds.

Another means to write this would certainly be 5/3, or five-thirds. These two numbers look different, but they're in reality the same. 5/3 is one improper fraction. This just means the numerator is larger than the denominator.

There are times as soon as you might prefer to use an improper portion instead the a blended number. It's basic to readjust a combined number into an not correct fraction. Let's find out 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 find out how plenty of parts comprise the whole number: 1 in this example.

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To carry out this, we'll main point the whole number, 1, through the denominator, 4.

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1 time 4 equates to 4.

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

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4 plus 1 amounts to 5.

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The denominator remains the same.

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

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

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

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First, we'll main point the totality number through the denominator. 2 time 5 amounts to 10.

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

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As always, the denominator will remain 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 wrong fractions right into mixed numbers

Improper fountain are beneficial for math difficulties that usage fractions, together you'll learn later. However, they're additionally more difficult to read and understand than mixed numbers. Because that example, it's a lot simpler to snapshot 2 4/7 in your head than 18/7.

Click v the slideshow come learn exactly how to readjust an improper fraction into a combined number.

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

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You can think of any fraction as a division problem. Just treat the line in between the numbers choose a division sign (/).

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

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10 split by 4 amounts to 2...

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

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The answer, 2, will end up being our totality number because 10 can be divided by 4 twice.

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And the remainder, 2, will end up being the numerator of the portion because we have 2 components 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 try another example: 33/3.

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

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33 separated by 3...

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

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

See more: What Abiotic Factors In The Pacific Ocean Zones? Ocean Abiotic Factors

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