Comparing Fractions

🏆Practice comparison of fractions

Comparing Fractions

How do you compare fractions?

The first step -

Find a common denominator – by expanding and reducing or by multiplying the denominators. (Remember to multiply both the numerator and the denominator)

The second step -

Let's check which fraction is larger based on the numerators alone. The fraction with the larger numerator will be larger.

Note- First of all, we will convert whole numbers and mixed numbers to improper fractions, and only then will we find a common denominator.

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Test yourself on comparison of fractions!


Fill in the missing sign:

\( \frac{5}{25}☐\frac{1}{5} \)

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Comparing Fractions

To compare fractions, all we need to do is find a common denominator – that is, bring both fractions to a state where the denominators are the same.
Then, we compare the numerators. The fraction with the larger numerator will be the greater one.

  • If there is a mixed fraction or a whole number - we will convert them to improper fractions and only then find a common denominator.

How do you find a common denominator?

A common denominator will be – the product of the denominators! (Remember that we multiply both the numerator and the denominator)
Sometimes, we won't need to multiply the denominators and can perform an operation on just one fraction (expansion or reduction – in cases where one fraction already has the common denominator in the denominator).
In any case, we need to bring both fractions to the same denominator.

Let's practice:
Mark the correct sign >,<,=>,<,=

Let's look at the two fractions and notice that 44 is the common denominator.
Since 44 is in the denominator of one of the fractions, we will need to multiply the numerator and denominator of the other fraction - 121 \over 2 by 22
We get:
343 \over 4______________242 \over 4

Now, since the denominators are the same, we can just compare the numerators to find out which is greater. Since 33 is greater than 22, the sign will be >>.

Another exercise:
Mark the correct sign >,<,=>,<,=

We can immediately see that it is 1=11=1 and that the fractions are identical (any number divided by itself equals 11), but we will still follow the method and find a common denominator.
The common denominator will be 44 and we get:
444 \over 4_____________444 \over 4

Now it can be clearly seen that the fractions are identical.

Mark the correct sign >,<,=>,<,=

Find a common denominator by multiplying the denominators.
Multiply the fraction 343 \over 4 by 55, the denominator of the second fraction, and the fraction 545 \over 4.
Multiply by 44, the denominator of the other fraction.
Remember! – Multiply both the numerator and the denominator.
We get:
152015 \over 20___________________162016 \over 20

Now we compare based on the numerators only. 1616 is greater than 1515 and therefore the sign is <<

Another exercise:
Mark the correct sign >,<,=>,<,=

1121 \frac{1}{2}_____________________2262\frac{2}{6}

Since we see mixed numbers in the exercise, we automatically convert them to improper fractions.


Let's rewrite the exercise:

We find a common denominator by multiplying the denominators and we get:
281228 \over 12___________________181218 \over 12
We compare the numerators, and therefore the sign will be >>

  • Note - if you found a different common denominator – for example 6, that's perfectly fine and as long as you found it correctly, it's not a mistake.

Another exercise:
Mark the correct sign >,<,=>,<,=

33_____________________626 \over 2

We will convert the whole number 33 into a fraction - 313 \over 1 and rewrite the exercise:

Now we will find the common denominator 2 and we get:

626 \over 2_____________________626 \over 2
The fractions are identical, so the sign will be ==.

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