Is 3 6 Greater Than 1 2? Top Answer Update

How do you compare fractions?

The answer to this question depends on whether you are comparing fractions with the same denominator or fractions with different denominators.

Compare fractions with the same denominator

Comparing fractions with the same denominator (bottom number) is easy. All you do is compare the numerators to see which fraction is larger, like so:

Same denominators

4 > 3 5 5 comparison with denominators

Compare fractions with different denominators

Comparing fractions with different denominators takes a bit more work (unless you’re using the fraction comparison calculator on this page), because to compare the fractions, you first need to convert their different denominators into the same denominators. You do this by finding the least common multiple (LCM) of the denominators.

To illustrate how to use LCM to convert different denominators into equal denominators, let’s say you want to compare the fraction 2/3 to the fraction 3/4 to see which is larger.

The first step is to find the lowest number that both 3 and 4 divide evenly into (the LCM). According to my calculations, the LCM of the two denominators (3 & 4) is 12.

Once we have found the LCM for the two denominators, the next step is to multiply the top and bottom of each fraction by the number that each fraction’s denominator goes into the LCM.

Since 3 goes into 12 a total of 4 times, you would multiply the top and bottom of 2/3 by 4, giving 8/12.

Next, since 4 goes into 12 a total of 3 times, you would multiply the top and bottom of 3/4 by 3, giving 9/12.

Finally, since both denominators are the same, you compare the numerators (8 and 9) to determine which fraction is larger. Since 9 is greater than 8, 9/12 is greater than 8/12—so 3/4 is greater than 2/3. Here is what our example of comparing fractions with different denominators might look like on paper:

Step #1: 2x 4 vs 3x 3 = 8 vs 9 3x 4 4x 3 12 12

Step #2: Compare 8 < 9 12 12 fractions with different denominators So for equal denominators you just compare the numerators and for unequal denominators you multiply the top and bottom by the least common multiple of each denominator and then compare the numerators. Which fraction is larger calculator Is 1/1 1/2 2/2 1/3 2/3 3/3 1/4 2/4 3/4 4/4 1/5 2/5 3/5 4/5 5/5 1/6 2 /6 3/6 4/6 5/6 6/6 1/7 2/7 3/7 4/7 5/7 6/7 7/7 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 9/9 1/10 2/10 3/10 4/10 5/ 10 6/10 7/10 8/10 9/10 10/10 greater than 1/1 1/2 2/2 1/3 2/3 3/3 1/4 2/4 3/4 4/4 1/ 5 2/5 3/5 4/5 5/5 1/6 2/6 3/6 4/6 5/6 6/6 1/7 2/7 3/7 4/7 5/7 6/7 7 /7 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 9/9 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10 ? Answer: Yes, 3/4 is greater than 1/2. You can confirm this by converting both fractions to decimals. 3/4 = 0.75 1/2 = 0.5 The decimal number 0.75 is greater than 0.5, so 3/4 is greater than 1/2. Greater than less than fraction calculator The calculator below generates a list of fractions that are greater or less than the selected fraction between 1/1 and 20/20.

It can be difficult to remember which inequality sign or symbol to use in a number comparison, but we have a simple memory trick that can help!

Notice how the inequality symbol has a wide end and a narrow end?

The wide end opens to the larger value and the narrow end points to the smaller value. If we describe the image below from left to right, it reads that all spider people are bigger (or taller) than just a spider ham.

If we flip things around, we can still read it left-to-right, but now it reads like one Spider-Ham is smaller (or smaller) than all of the Spider People.

wide end

open for

larger number

How do we find the larger number? 🕵🏿‍♀️

The larger digit is farther from 0 on the number line. When we compare numbers, we compare place values ​​from left to right. The number that has the first place value with a on the number line. The number furthest to the right on the number line is the larger number. − 4 − 3 − 2 − 1 0 1 2 3 4 Move left Move right Remember that numbers are larger further to the right, by imagining a phone’s signal bars – the bars get bigger and stronger the further we go go right. This also means that any positive number is greater than any negative number 💡. Why is a larger negative number smaller than a smaller negative number? 🤔 Remember that as we move right on the number line, the numbers get bigger. For negative numbers, you can think of “greater than” as meaning “which number is less negative (or more positive)”. − 7 − 2 0 − 2 > − 7 Since −2 is further to the right than −7, −2 is greater than −7. Calculator Calculator Lesson Practice Practice Check out our or the and sections to learn more about comparing numbers, fractions and decimals and test your understanding. Explore Calculator

We can apply the same concept to comparing numbers. The sign should always be that

Lesson 2: Compare and reduce fractions

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compare fractions

In Introduction to Fractions, we learned that fractions are a way of representing a part of something. Fractions are useful because they tell us exactly how much we have of something. Some fractions are larger than others. For example, which is larger: 6/8ths of a pizza or 7/8ths of a pizza?

In this image we can see that 7/8 is larger. The figure makes it easy to compare these fractions. But how could we have done that without the pictures?

Click through the slideshow to learn how to compare fractions.

We have already seen that fractions have two parts.

One part is the top number or numerator.

The other is the bottom number or denominator.

The denominator tells us how many parts a whole has.

The counter tells us how many of these parts we have.

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

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

Here 5 is more than 4…

Here 5 is more than 4… so we can say that 5/6 is more than 4/6.

Let’s look at another example. Which of these is bigger: 2/8 or 6/8?

If you thought 6/8 was bigger, you were right!

Both fractions have the same denominator.

So we compared the counters. 6 is greater than 2, so 6/8 is more than 2/8.

As you’ve seen, when two or more fractions have the same denominator, you can compare them by looking at their numerators. As you can see below, 3/4 is larger than 1/4. The larger the numerator, the larger the fraction.

Comparing fractions with different denominators

On the previous page we compared fractions that have the same lower numbers or denominators. But you know that fractions can have any number as a denominator. What if you need to compare fractions with different lower numbers?

For example, which of these is larger: 2/3 or 1/5? It’s hard to tell just by looking at her. After all, 2 is greater than 1, but the denominators are not equal.

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

Click through the slideshow to learn how to compare fractions with different denominators.

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

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

First we find the smallest number that can be divided by both denominators. This is what we call the lowest common denominator.

Our first step is to find numbers that are divisible by 8.

Using a multiplication table makes this easy. All numbers in the 8-series can be divided by 8 without a remainder.

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

We can use the multiplication table again. All numbers in the 6-series can be divided by 6 without a remainder.

Let’s compare the two lines. It looks like there are some numbers that are divisible by both 6 and 8.

24 is the smallest number that occurs in both series, so the lowest common denominator.

Now let’s change our fractions so that they both have the same denominator: 24.

To do this, we need to change the numerators in the same way we changed the denominators.

Let’s look at 5/8 again. To change the denominator to 24…

Let’s look at 5/8 again. To change the denominator to 24…we had to multiply 8 by 3.

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

5 times 3 equals 15. So we changed 5/8 to 15/24.

We can because every number over itself is equal to 1.

So if we multiply 5/8 by 3/3…

So when we multiply 5/8 by 3/3, we’re really multiplying 5/8 by 1.

Since every number times 1 is equal to itself…

Since any number times 1 equals itself, we can say that 5/8 equals 15/24.

Now let’s do the same with our other fraction: 4/6. We also changed its denominator to 24.

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

So we also multiply the numerator by 4.

4 times 4 is 16. So 4/6 equals 16/24.

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

16/24 is greater than 15/24…

16/24 is greater than 15/24… so 4/6 is greater than 5/8.

reduce fractions

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

If you did the math or just looked at the picture you might have been able to tell that they are the same. In other words, 4/8 and 1/2 mean the same thing, even though they’re spelled differently.

If 4/8 means the same as 1/2, why not just call it that? One half is easier to say than four eighths, and it’s also easier for most people to understand. After all, when dining out with a friend, split the bill in half, not eighths.

If you write 4/8 as 1/2, reduce it. When we shorten a fraction, we write it in a simpler form. Reduced fractions are always equal to the original fraction.

We have already reduced 4/8 to 1/2. If you look at the examples below, you can see that other numbers can be reduced to 1/2 as well. These fractions are all the same.

5/10 = 1/2

22.11 = 1/2

36/72 = 1/2

These fractions have also all been reduced to a simpler form.

4/12 = 1/3

14/21 = 2/3

35/50 = 7/10

Click through the slideshow to learn how to reduce fractions by dividing.

Let’s try to reduce this fraction: 16/20.

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

First we divide the numerator by 2. 16 divided by 2 equals 8.

Next we divide the denominator by 2. 20 divided by 2 equals 10.

We reduced 16/20 to 8/10. We could also say that 16/20 equals 8/10.

If the numerator and denominator are still divisible by 2, we can further reduce the fraction.

8 divided by 2 is 4.

10 divided by 2 is 5.

Since there is no number by which 4 and 5 can be divided, we cannot reduce 4/5 any further.

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

Let’s try reducing another fraction: 6/9.

While the numerator is even, the denominator is an odd number, so we can’t reduce by dividing by 2.

Instead, we need to find a number by which 6 and 9 can be divided. A multiplication table makes this number easy to find.

Let’s find 6 and 9 in the same row. As you can see, 6 and 9 can both be divided by 1 and 3.

Dividing by 1 doesn’t change these fractions, so we use the largest number that 6 and 9 can be divided by.

That’s 3. This is called the greatest common divisor, or gcd. (It can also be called the greatest common factor or GCF.)

3 is the gcd of 6 and 9 because it’s the largest number they can be divided by.

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

Then we divide the denominator by 3. 9 divided by 3 is 3.

Now we’ve reduced 6/9 to 2/3, which is the simplest form. We could also say that 6/9 equals 2/3.

Irreducible fractions

Not all fractions can be reduced. Some are already as simple as they can be. For example, you can’t cancel 1/2 because there is no number other than 1 that can divide both 1 and 2. (For this reason, you cannot reduce a fraction that has a numerator of 1.)

Also, some fractions with larger numbers cannot be reduced. For example, 17/36 cannot be reduced because there is no number by which both 17 and 36 can be divided. If you can’t find common multiples for the numbers in a fraction, it’s probably irreducible.

Try this!

Reduce each fraction to its simplest form.

Mixed numbers and improper fractions

In the previous lesson, you learned about mixed numbers. A mixed number has both a fraction and a whole number. An example is 1 2/3. You would read 1 2/3 like this: one and two thirds.

Another spelling would be 5/3 or five thirds. These two numbers look different but are actually the same. 5/3 is an improper fraction. It just means that the numerator is greater than the denominator.

There are times when you might prefer to use an improper fraction instead of a mixed number. It’s easy to convert a mixed number to an improper fraction. Let’s learn how:

Let’s convert 1 1/4 to an improper fraction.

First we need to figure out how many parts make up the whole number: 1 in this example.

To do this, we multiply the whole number , 1, by the denominator 4.

1 times 4 equals 4.

Now let’s add this number, 4, to the numerator 1.

4 plus 1 equals 5.

The denominator stays the same.

Our improper fraction is 5/4, or five quarters. So we could say that 1 1/4 equals 5/4.

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

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

First we multiply the whole number by the denominator. 2 times 5 equals 10.

Next we add 10 to the numerator. 10 plus 2 equals 12.

The denominator remains the same as always.

So 2 2/5 equals 12/5.

Try this!

Try converting these mixed numbers to improper fractions.

Convert improper fractions to mixed numbers

Improper fractions are useful for math problems that use fractions, as you’ll learn later. However, they are also more difficult to read and understand than mixed numbers. For example, it is much easier to visualize 2 4/7 in your head than 18/7.

Click through the slideshow to learn how to convert an improper fraction to a mixed number.

Let’s turn 10/4 into a mixed number.

You can think of every fraction as a division problem. Just treat the dash between the numbers like a division sign (/).

So we divide the numerator 10 by the denominator 4.

10 divided by 4 equals 2…

10 divided by 4 gives 2… with remainder 2.

The answer 2 becomes our integer because 10 can be divided by 4 twice.

And the remainder, 2, becomes the numerator of the fraction because we have 2 parts left.

The denominator stays the same.

So 10/4 equals 2 2/4.

Let’s try another example: 33/3.

We divide the numerator 33 by the denominator 3.

33 divided by 3…

33 divided by 3…is 11 with no remainder.

The answer, 11, becomes our integer.

There’s no remainder, so we can see that our improper fraction was actually an integer. 33/3 equals 11.

Try this!

Try converting these improper fractions into mixed numbers.

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Question:

Is 5/6 greater or less than 2/3?

Order and compare fractions:

When ordering fractions, order them from smallest amount to largest amount. When you compare fractions, you identify which of the given fractions are the smallest or the largest. The easiest way to do this is to first convert the fractions so that they have the same denominator.

Answer and explanation: 1

Become a Study.com member to unlock this answer! Create your account. Check out this answer

If we want to compare two fractions, we must have the same denominator. So we need the LCM (least common multiple) of #4# and #3#, which is #12#. So we need to multiply 4 by #3# and 3 by #4#

Remember that whatever you do below must be done above.

For #3/4# we multiply 3 down (denominator), so we need to multiply #3# up (numerator).

For #2/3# we multiply #4# down, so we need to multiply #4# up.

#(3xx3)/(4xx3)=9/12# and #(2xx4)/(3xx4)=8/12#

Now just look at the counts of the two answers. #9# is bigger than #8#, so #9/12# is bigger! #9/12# was originally #3/4# .

So #3/4# is greater than #2/3# .

I hope you understood this and my source is my knowledge!

If we want to compare two fractions, we must have the same denominator. So we need the LCM (least common multiple) of #4# and #3#, which is #12#. So we need to multiply 4 by #3# and 3 by #4#

Remember that whatever you do below must be done above.

For #3/4# we multiply 3 down (denominator), so we need to multiply #3# up (numerator).

For #2/3# we multiply #4# down, so we need to multiply #4# up.

#(3xx3)/(4xx3)=9/12# and #(2xx4)/(3xx4)=8/12#

Now just look at the counts of the two answers. #9# is bigger than #8#, so #9/12# is bigger! #9/12# was originally #3/4# .

So #3/4# is greater than #2/3# .

I hope you understood this and my source is my knowledge!

Lesson 2: Compare and reduce fractions

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compare fractions

In Introduction to Fractions, we learned that fractions are a way of representing a part of something. Fractions are useful because they tell us exactly how much we have of something. Some fractions are larger than others. For example, which is larger: 6/8ths of a pizza or 7/8ths of a pizza?

In this image we can see that 7/8 is larger. The figure makes it easy to compare these fractions. But how could we have done that without the pictures?

Click through the slideshow to learn how to compare fractions.

We have already seen that fractions have two parts.

One part is the top number or numerator.

The other is the bottom number or denominator.

The denominator tells us how many parts a whole has.

The counter tells us how many of these parts we have.

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

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

Here 5 is more than 4…

Here 5 is more than 4… so we can say that 5/6 is more than 4/6.

Let’s look at another example. Which of these is bigger: 2/8 or 6/8?

If you thought 6/8 was bigger, you were right!

Both fractions have the same denominator.

So we compared the counters. 6 is greater than 2, so 6/8 is more than 2/8.

As you’ve seen, when two or more fractions have the same denominator, you can compare them by looking at their numerators. As you can see below, 3/4 is larger than 1/4. The larger the numerator, the larger the fraction.

Comparing fractions with different denominators

On the previous page we compared fractions that have the same lower numbers or denominators. But you know that fractions can have any number as a denominator. What if you need to compare fractions with different lower numbers?

For example, which of these is larger: 2/3 or 1/5? It’s hard to tell just by looking at her. After all, 2 is greater than 1, but the denominators are not equal.

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

Click through the slideshow to learn how to compare fractions with different denominators.

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

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

First we find the smallest number that can be divided by both denominators. This is what we call the lowest common denominator.

Our first step is to find numbers that are divisible by 8.

Using a multiplication table makes this easy. All numbers in the 8-series can be divided by 8 without a remainder.

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

We can use the multiplication table again. All numbers in the 6-series can be divided by 6 without a remainder.

Let’s compare the two lines. It looks like there are some numbers that are divisible by both 6 and 8.

24 is the smallest number that occurs in both series, so the lowest common denominator.

Now let’s change our fractions so that they both have the same denominator: 24.

To do this, we need to change the numerators in the same way we changed the denominators.

Let’s look at 5/8 again. To change the denominator to 24…

Let’s look at 5/8 again. To change the denominator to 24…we had to multiply 8 by 3.

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

5 times 3 equals 15. So we changed 5/8 to 15/24.

We can because every number over itself is equal to 1.

So if we multiply 5/8 by 3/3…

So when we multiply 5/8 by 3/3, we’re really multiplying 5/8 by 1.

Since every number times 1 is equal to itself…

Since any number times 1 equals itself, we can say that 5/8 equals 15/24.

Now let’s do the same with our other fraction: 4/6. We also changed its denominator to 24.

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

So we also multiply the numerator by 4.

4 times 4 is 16. So 4/6 equals 16/24.

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

16/24 is greater than 15/24…

16/24 is greater than 15/24… so 4/6 is greater than 5/8.

reduce fractions

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

If you did the math or just looked at the picture you might have been able to tell that they are the same. In other words, 4/8 and 1/2 mean the same thing, even though they’re spelled differently.

If 4/8 means the same as 1/2, why not just call it that? One half is easier to say than four eighths, and it’s also easier for most people to understand. After all, when dining out with a friend, split the bill in half, not eighths.

If you write 4/8 as 1/2, reduce it. When we shorten a fraction, we write it in a simpler form. Reduced fractions are always equal to the original fraction.

We have already reduced 4/8 to 1/2. If you look at the examples below, you can see that other numbers can be reduced to 1/2 as well. These fractions are all the same.

5/10 = 1/2

22.11 = 1/2

36/72 = 1/2

These fractions have also all been reduced to a simpler form.

4/12 = 1/3

14/21 = 2/3

35/50 = 7/10

Click through the slideshow to learn how to reduce fractions by dividing.

Let’s try to reduce this fraction: 16/20.

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

First we divide the numerator by 2. 16 divided by 2 equals 8.

Next we divide the denominator by 2. 20 divided by 2 equals 10.

We reduced 16/20 to 8/10. We could also say that 16/20 equals 8/10.

If the numerator and denominator are still divisible by 2, we can further reduce the fraction.

8 divided by 2 is 4.

10 divided by 2 is 5.

Since there is no number by which 4 and 5 can be divided, we cannot reduce 4/5 any further.

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

Let’s try reducing another fraction: 6/9.

While the numerator is even, the denominator is an odd number, so we can’t reduce by dividing by 2.

Instead, we need to find a number by which 6 and 9 can be divided. A multiplication table makes this number easy to find.

Let’s find 6 and 9 in the same row. As you can see, 6 and 9 can both be divided by 1 and 3.

Dividing by 1 doesn’t change these fractions, so we use the largest number that 6 and 9 can be divided by.

That’s 3. This is called the greatest common divisor, or gcd. (It can also be called the greatest common factor or GCF.)

3 is the gcd of 6 and 9 because it’s the largest number they can be divided by.

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

Then we divide the denominator by 3. 9 divided by 3 is 3.

Now we’ve reduced 6/9 to 2/3, which is the simplest form. We could also say that 6/9 equals 2/3.

Irreducible fractions

Not all fractions can be reduced. Some are already as simple as they can be. For example, you can’t cancel 1/2 because there is no number other than 1 that can divide both 1 and 2. (For this reason, you cannot reduce a fraction that has a numerator of 1.)

Also, some fractions with larger numbers cannot be reduced. For example, 17/36 cannot be reduced because there is no number by which both 17 and 36 can be divided. If you can’t find common multiples for the numbers in a fraction, it’s probably irreducible.

Try this!

Reduce each fraction to its simplest form.

Mixed numbers and improper fractions

In the previous lesson, you learned about mixed numbers. A mixed number has both a fraction and a whole number. An example is 1 2/3. You would read 1 2/3 like this: one and two thirds.

Another spelling would be 5/3 or five thirds. These two numbers look different but are actually the same. 5/3 is an improper fraction. It just means that the numerator is greater than the denominator.

There are times when you might prefer to use an improper fraction instead of a mixed number. It’s easy to convert a mixed number to an improper fraction. Let’s learn how:

Let’s convert 1 1/4 to an improper fraction.

First we need to figure out how many parts make up the whole number: 1 in this example.

To do this, we multiply the whole number , 1, by the denominator 4.

1 times 4 equals 4.

Now let’s add this number, 4, to the numerator 1.

4 plus 1 equals 5.

The denominator stays the same.

Our improper fraction is 5/4, or five quarters. So we could say that 1 1/4 equals 5/4.

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

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

First we multiply the whole number by the denominator. 2 times 5 equals 10.

Next we add 10 to the numerator. 10 plus 2 equals 12.

The denominator remains the same as always.

So 2 2/5 equals 12/5.

Try this!

Try converting these mixed numbers to improper fractions.

Convert improper fractions to mixed numbers

Improper fractions are useful for math problems that use fractions, as you’ll learn later. However, they are also more difficult to read and understand than mixed numbers. For example, it is much easier to visualize 2 4/7 in your head than 18/7.

Click through the slideshow to learn how to convert an improper fraction to a mixed number.

Let’s turn 10/4 into a mixed number.

You can think of every fraction as a division problem. Just treat the dash between the numbers like a division sign (/).

So we divide the numerator 10 by the denominator 4.

10 divided by 4 equals 2…

10 divided by 4 gives 2… with remainder 2.

The answer 2 becomes our integer because 10 can be divided by 4 twice.

And the remainder, 2, becomes the numerator of the fraction because we have 2 parts left.

The denominator stays the same.

So 10/4 equals 2 2/4.

Let’s try another example: 33/3.

We divide the numerator 33 by the denominator 3.

33 divided by 3…

33 divided by 3…is 11 with no remainder.

The answer, 11, becomes our integer.

There’s no remainder, so we can see that our improper fraction was actually an integer. 33/3 equals 11.

Try this!

Try converting these improper fractions into mixed numbers.

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I recently read the book Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense by Julie McNamara and Meghan Shaughnessy.

I posted the following image on Twitter while reading during my daughter’s swim class.

My colleague Hedge replied that he was challenged by a middle school teacher on this very subject.

I let them know that a few years ago, when I was a digital curriculum developer, I was also challenged for this idea. The argument I heard at the time was that using context to check the correctness of fractional comparisons would be against the fact that fractions are numbers. Therefore, 1/2 is always greater than 1/3, regardless of context. I wondered about that at the time, but I still felt it was important to show context.

Jump ahead and I’ve been thinking about this idea all day. I think I finally understand why we need to be careful about what we say about the role of context when comparing fractions. I may be completely off the mark, but I’ll still share my thoughts and let you decide in the comments whether you want to challenge my thoughts or share an alternative point of view.

Let’s start with whole numbers. If I told you to compare 3 and 6, you would probably say “3 is less than 6” or “6 is greater than 3”. This is how the numbers 3 and 6 are related.

Now what if I showed you these two pictures of 3 and 6: (As illustrated by my daughter’s toys.)

Technically the 3 dolls are bigger and therefore make up more stuff, but does that really mean that 3 is now bigger than 6? In the end, my daughter has fewer dolls (3) than figures (6). The context does not fundamentally change the relationship between the numbers 3 and 6.

In this case I don’t even know how to justify that she has more when I refer to the dolls. Sure, they’re bigger, but she might prefer to have more things to play with, and chooses the 6 figures even though they’re smaller overall.

Let’s continue by looking at this from a fractional perspective. Now I take 1/3 of the dolls and 1/2 of the figures.

Consistent with the idea that context should determine when one number is larger than another, I should be confident that 1/3 of the puppets is larger than 1/2 of the figures because 1 puppet is so much larger than the 3 characters. Oh wait, or should I be thinking that 1/2 of the figures is larger than 1/3 of the dolls because I ended up with 3 figures, which is a larger number of things than 1 doll? It’s not that clear cut, even if I try to let the context dictate how to interpret the fractions.

It boils down to breaks representing a relationship. When I think about the relationships each fraction represents, 1/2 is always greater than 1/3 no matter how I try to rotate it. Looking back at my examples, taking 1/2 of the figurine group means I’m taking a larger proportion of that group (this whole) than if I take 1/3 of the puppet group (a different whole, but still a whole) . The size of things in my group (total) doesn’t matter because the relationship represented by 1/2 is larger than the relationship represented by 1/3.

Does this mean that we should ignore contexts altogether? no There’s still a lot of debate about who ate more pizza when one person eats half of a small pizza and another person eats a third of a large pizza. Context is still interesting to discuss and helps students use math to interpret the world around them. However, if our goal is to compare fractions, then 1/2 is greater than 1/3 every time.

That’s the argument I came up with today, trying to understand the criticism I’ve heard. Now that you’ve read it, what do you think?

Written by Priya_Singh

Last modified on 07/20/2022

compare fractions

Comparing Fractions: When it comes to fractions, we usually compare two or more fractions. In fact, we experience ruptures in our daily lives. A simple example, if you cut an apple in two, it’s also a fraction. Basically, comparing two fractions means determining the major and minor fractions among them. Let’s learn more about fractions and how they compare. In this article, you will get details on definition of fractions, how to compare fractions, rules to compare fractions, decimal method to compare fractions and solved examples for faster and better understanding.

At Embibe, we strongly encourage you to learn the basic concept behind fractions as this is an important aspect of algebra. Reading through the basics of fractions and how to compare them and what unlike and similar fractions are will help you understand algebra better. Read the full article to get complete knowledge.

define fractions

A fraction is a number that represents part of the whole. This whole can be a single object or a group of objects. A fraction is written as \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q

e 0\). Numbers like \(\frac{1}{2},\frac{2}{3},\frac{4}{5},\frac{{11}}{7}\) are called fractions.

The number below the division line is called the denominator. It tells us how many equal parts a whole is divided into. The number above the line is called the counter. It tells us how many equal parts are taken.

Examples: \(\frac{3}{7},\frac{5}{{10}} = \frac{{11}}{4}\)etc. are some of the examples of the fractions.

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How do you compare fractions?

Now that you understand what a fraction is? Let us tell you how to compare fractions. As you already know, a fraction is nothing more than a part of a whole object. So if you break the glass bowl into multiple pieces, can you still say that each element represents the break?

Yes you can. Any element can still be reasonably referred to as a fraction of the glass bowl, but a fraction comes with a rule in math. The rule is, “All parts must be equal.” So a fraction has two parts; they are called numerator and denominator.

Now let’s discuss what comparing fractions means when comparing the two bits to find out which is larger or smaller. Real-time fraction comparison examples include various activities like checking discount prices when shopping, achieving sales of a specific product, doctor’s medical prescriptions, numerous tests and exams, etc. So, let’s go through the different fraction comparison methods with examples to better understand the concept. Again, comparing fractions or fractions is what you experience or deal with in your daily life. If you focus enough, you can get a practical understanding of it every day while doing ordinary chores and math calculations.

Compare fractions rules

There are a few rules we need to keep in mind when comparing fractions:

1. When the denominators of the fraction are the same, the fraction with the smaller numerator is considered the smaller fraction, and the fraction with the larger numerator is considered the larger fraction.

2. If the numerators are equal, the fractions are considered equivalent.

If the fractions have the same numerator, the smaller denominator is considered the more significant fraction.

Compare fractions with the same denominator

Definition of equal fractions: Two or more fractions with the same dominator are called “equal fractions”.

Example: \(\frac{3}{{11}},\frac{{15}}{{11}} = \frac{{ – 9}}{{11}}\) are “like fractions”.

Compare equal fractions

In this method, you need to check whether the denominators are equal or not. If the denominators are the same, then the fraction with the larger numerator is the larger fraction. The fraction with the smaller numerator is the smaller fraction. If the numerator and denominator are the same, then the fractions are the same. For example: Let’s compare \(\frac{6}{{17}}\) and \(\frac{{16}}{{17}}\).

Find the denominators of the given fractions: \(\frac{6}{{17}}\) and \(\frac{{16}}{{17}}\). Here the denominators are the same. Next, compare the counters \(16 > 6\). Now, with the larger numerator, the fraction would be larger. So \(\frac{6}{{17}} < \frac{{16}}{{17}}}\). Comparing fractions with different denominators Definition of an unequal fraction: When two or more fractions have a different denominator, this is called "unequal fractions". Example: \(\frac{3}{5},\frac{7}{{11}}, – \frac{2}{4},\frac{{39}}{{14}}}\) are not equal fractions. Comparing unlike fractions To compare the fractions with different denominators, we suggest you find the lowest common denominator (LCM) first to make the denominators equal. If the denominators are converted to the same denominator, then the fraction with the larger numerator is the more significant fraction — for example, \(\frac{1}{2}\) and \(\frac{2}{5}\ ). Look for the denominators of the given fractions, \(\frac{1}{2}\) and \(\frac{2}{5}\) here, the denominators are not equal. Next, take out the LCM of \(2 & 5\), i.e. \({\mathop{\rm LCM} bounds} (2,5) = 10\). Here \(\frac{1}{2} = \frac{1}{2} \times \frac{5}{5}\) and \(\frac{2}{5} = \frac{2} {5} \times \frac{2}{2}\). Now compare the fractions, \(\frac{5}{{10}}\) and \(\frac{4}{{10}}\), so that the denominators are the same. We will compare the numerators, \({\rm{5 > 4}}{\rm{.}}\). Compare the fractions, \(\frac{5}{{10}} > \frac{4}{{10}}\) . The larger numerator fraction is the larger fraction. So \(\frac{5}{{10}} > \frac{4}{{10}}\). So \(\frac{1}{2} > \frac{2}{5}\)

When the denominators are different and the numerators are the same, you can easily compare fractions by looking at their denominators. The fraction with the smaller denominator has a larger value. The fraction with a larger denominator has a smaller value.

Example: \(\frac{2}{3} > \frac{2}{6}\)

Decimal method for comparing fractions

This method requires you to compare the decimal values ​​of the fractions. First the numerator is divided by the denominator and then the fraction is converted to a decimal. Then the decimal values ​​are compared.

Example: \(\frac{4}{5}\) and \(\frac{6}{8}\)

First write the given fractions \(\frac{4}{5}\) and \(\frac{6}{8}\) in decimal form. \(\frac{4}{5} = 0.8\) and \(\frac{6}{8} = 0.75\). Now compare the decimal values, \(0.8 > 0.75\). Here, the fraction with the larger decimal value is the larger fraction. So \(\frac{4}{5} > \frac{6}{8}\).

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Comparing fractions with cross multiplication

In this method, the numerator of one fraction is cross-multiplied by the denominator of the other fraction. For example, the arrows indicated the same thing in the diagram given below.

Example: If we multiply, we get \(4\) and \(6\).

1. Well, the numbers \(4\) and \(6\) are the numerators we get if we use \(\frac{1}{2}\) and \(\frac{3}{4} \ have expressed ) with the common denominator \(8\).

2. Next, the new fractions with the same denominators will be \(\frac{4}{8}\) and \(\frac{6}{8}\).

3. So the number 6 is the larger numerator, \(\frac{4}{8} < \frac{6}{8}\). 4. So \(\frac{1}{2} < \frac{3}{4}\). Solved examples - compare fractions Q.1. Compare the two fractions \(\frac{4}{7}\) and \(\frac{2}{7}\). Answer: Given \(\frac{4}{7}\) and \(\frac{2}{7}\) We can see that the denominators in the given fractions are equal. Here we follow the rule that when the denominators of the fraction are equal, the fraction with the smaller numerator is considered the smaller fraction and the fraction with the larger numerator is considered the larger fraction. So compare the counters \(4 > 2\)

So \(\frac{4}{7} > \frac{2}{7}\)

F.2. Compare the two given fractions: \(\frac{6}{{13}}\) and \(\frac{6}{{20}}\)

Answer: Given \(\frac{6}{{13}}\) and \(\frac{6}{{20}}\)

We can see that the numerators in the given fractions are equal.

Here we follow the rule that for fractions with the same numerator, the smaller denominator is considered the larger fraction.

So compare the denominators \(13 > 20\)

So \(\frac{6}{{13}} > \frac{6}{{20}}\)

F.3. Compare the given fractions using the cross multiplication method: \(\frac{3}{8}\) and \(\frac{5}{{10}}\)

Answer: Given \(\frac{3}{8}\) and \(\frac{5}{{10}}\)

We will use the cross multiplication method,

So \(\frac{3}{8} \to \frac{5}{{10}}\), which means multiply \(3 \times 10 = 30\)

Well, \(\frac{3}{8} \leftarrow \frac{5}{{10}}\), which means multiply \(5 \times 8 = 40.\)

Here \(30 < 40\) So \(\frac{3}{8} < \frac{5}{{10}}\) F.4. Arrange the fractions \(\frac{5}{6},\frac{{11}}{{16}},\frac{{13}}{{18}}\) in ascending order Answer: We will first take out the LCM of denominators, \(6,16,18 = 2 \times 3 \times 8 \times 3 = 144\) Now write the fractions as equivalents like fractions. \(\frac{5}{6} = \frac{{5 \times 24}}{{6 \times 24}} = \frac{{120}}{{144}},\frac{{11}} {{16}} = \frac{{11 \times 9}}{{16 \times 9}} = \frac{{99}}{{144}},\frac{{13}}{{18}} = \frac{{13 \times 8}}{{18 \times 8}} = \frac{{104}}{{144}}.\) So \(99 < 104 < 120 \Rightarrow \frac{{99}}{{144}} < \frac{{104}}{{144}} < \frac{{120}}{{144}} \ arrow to the right \frac{{11}}{{16}} < \frac{{13}}{{18}} < \frac{5}{6}\) Therefore the given fractions are in ascending order \(\frac{{11}}{{16}},\frac{{13}}{{18}},\frac{5}{6}\) F.5. Which is larger: \(\frac{4}{8}\) or \(\frac{6}{{12}}\) Compare with the decimal method. Answer: We can use a calculator \(4 \div 8\) and \(6 \div 12\) Now we get \(\frac{4}{8} = 0.5\) and \(\frac{6}{{12}} = 0.5\) So both fractions are equal \(\frac{4}{8} = \frac{6}{{12}}\) So \(\frac{4}{8} = \frac{6}{{12}}\) Try mock testing summary In this article, you learned how to compare fractions, a summary of what fractions are, and discussed the rules of fractions. Later we learned to compare equal fractions and unlike fractions. We also took a look at comparing fractions using cross multiplication and the decimal method, along with the solved examples and some of the frequently asked questions. Readers can compare fraction tricks to quickly solve the questions. frequently asked Questions Q.1. Which fractions are larger? Answer: To compare fractions with different denominators, convert them into equivalent fractions with the same denominator. If the denominators are the same, you can compare the numerators. The fraction with the larger numerator is the larger fraction. Q.2.What is the function of comparing fractions? Answer: Comparing fractions is easier when the denominators of the given fractions are the same. So if there is a group of equal fractions, they can easily be compared. For example, if you are comparing two fractions \(\frac{{21}}{{50}}\) and \(\frac{{37}}{{50}}\), you only need to compare the numerators. F.3. What are the tricks of comparing fractions? Answer: If you have two fractions, you can use a little trick to determine which fraction is larger. Example: Compare \(\frac{3}{8}\) and \(\frac{4}{9}\) Multiply the numerator of the first fraction (the top number in the fraction) by the denominator (the bottom number in the fraction) of the second fraction. Then compare the two answers. F.4. What does it mean to compare fractions? Answer: Comparing fractions means you want to determine if one fraction is less than, greater than, or equal to another. So we use symbols like with integers <, > or =

F.5. Give some examples of comparing fractions.

Answer: An example of comparing fractions is given below:

Example 1: \(\frac{4}{5}\) and \(\frac{6}{8}\)

1. First write the given fractions \(\frac{4}{5}\) and \(\frac{6}{8}\) in decimal form. \(\frac{4}{5} = 0.8\) and \(\frac{6}{8} = 0.75\).

2. Now compare the decimal values, \(0.8 > 0.75\).

3. Here, the fraction with the larger decimal value is the larger fraction.

4. So \(\frac{4}{5} > \frac{6}{8}\)

Example 2: If we multiply, we get \(4\) and \(6\).

1. Well, the numbers \(4\) and \(6\) are the numerators we get if we use \(\frac{1}{2}\) and \(\frac{3}{4} \ have expressed ) with the common denominator \(8\).

2. Next, the new fractions with the same denominators will be \(\frac{4}{8}\) and \(\frac{6}{8}\).

3. So the number \(6\) is the larger numerator, \(\frac{4}{8} < \frac{6}{8}\) 4. So \(\frac{1}{2} < \frac{3}{4}\) F.6. What are the two simple methods used to compare the fractions? Answer: The two methods used to compare fractions are simple 1. Decimal method and 2. Cross multiplication method F.7. What are the uses of comparing fractions? Answer: Comparing fractions helps us understand whether the given fractions are less than, greater than, or equal to. Just as we compare integers using the symbols \(<, >\) or \(=\), we use the same symbols to compare fractions.

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