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Compare fractions

You can learn how to compare fractions here. Let's look at this:

  • A Explanationhow to make fractions comparable.
  • Lots Examples to compare fractions.
  • Tasks / exercises so that you can practice comparing fractions yourself.
  • Videos for fractions.
  • A Question and answer area to this area.

Tip: If you have no idea about fractions, please take a look at the article Fractional calculation first. Otherwise, let's see how to compare fractions.

Explanation Compare fractions


In math, one sometimes wonders whether a fraction is smaller or larger than another fraction. If there are more than two fractions, you sometimes try to sort them according to size.
The simplest case for comparing fractions is two fractions with the same name. Fractions are referred to as having the same name if they have the same denominator. If this is the case, the comparison can be carried out very easily: You just look at the counter. The smaller numerator is the smaller fraction.

example 1:
Two fractions are to be compared with each other. Which fraction is bigger?

Solution:
We have two common denominators. Because of this, we simply see which numerator is larger to find the larger fraction. In math, there are signs for comparing numbers (and fractions). The simplest characters are smaller (<), larger (>) and equal (=). The larger number is on the left, so the ">" fits between the numbers.

Example 2:
The same counters can also make life a lot easier. All numerators are the same and the denominators are different. Let's take these two fractions as an example. Which one is smaller?

Solution:
The following applies: If two fractions have the same numerator, the fraction with the smaller denominator is the larger one.

Note:

Compare rules fractions:
  • If two fractions have the same numerator, the fraction with the smaller denominator is also the larger fraction.
  • If two fractions have the same denominator, the fraction with the smaller numerator is also the smaller fraction.
  • If two fractions have different numerators and denominators, the fractions are brought to a main denominator and then compared.

We'll look at the last of the three rules for comparison in the next section. Display:

Examples compare fractions

What happens in the case of fractions of a different name? So two (or more) fractions with different denominators. Let's start here with a simpler example.

Example 3:
We have two fractions with different denominators. Compare these two fractions and write the smaller number to the left.


Solution:
We have the denominators 3 and 6 for the fractions. To bring the fraction with 3 to the denominator 6, we have to multiply it by 2. We do the same with this fraction in the numerator. In the numerator we get 2 · 2 = 4 and in the denominator 3 · 2 = 6. Now we can see with the numerator that 4 is less than 5.


Example 4:
Now let's compare three fractions with different denominators. The largest fraction should be sorted to the left, the smallest fraction should be sorted to the right.

Solution:
With 4, 7 and 8 we have different denominators. We have to change this first and calculate a common main denominator. We do this with the least common multiple. To do this, we write down the multiples of 4, 7 and 8 and then look for the smallest number among the multiples.

The LCM - that is, the smallest common multiple - is thus 56. Next we have to calculate with which numbers we have to expand the fractions. We now take the new main denominator (56) and divide by 4, 7 and 8.


We expand the three fractions from the beginning with 14, 8 and 7.


Now let's compare. The larger the numerator, the larger the fraction.

Compare fractions practice exercises

Show:

Compare video fractions

Examples and explanations

The next video covers the following content about fractions:

  • Representation of fractions.
  • How do you compare fractions?
  • What do you have to consider with the numerator and denominator?
  • Examples are calculated.
  • Explanations are offered.

Next video »

Compare questions with answers fractions

In this section, we'll look at typical questions with answers about how to compare fractions.

Q: Can you compare fractions without giving them the same name?
A: There are several ways to do this:

  • Take another look at example 2 from above, where the counters were the same. Then you can see directly via the denominator which number is larger or smaller.
  • Another variant is to make decimal numbers (point numbers) out of them and then to compare them.
  • If you have a good mathematical idea, you can imagine the breaks in your head - for example as pizza - and compare them in your head.


Q: When is fractions comparing taught?
A: Fraction comparison is covered in middle school (5th grade, 6th grade, and sometimes 7th grade). Fractional equations are also taught in the intermediate level.

Q: Can you order one or more fractions on a number line / line?
A: Of course you can. You can see how this works under number line fractions.