Find a common denominator – by expanding and reducing or by multiplying the denominators. (Remember to multiply both the numerator and the denominator)
Find a common denominator – by expanding and reducing or by multiplying the denominators. (Remember to multiply both the numerator and the denominator)
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.
If the numerators are identical, the larger fraction is the one with the smaller denominator!
Sometimes, you can compare fractions by comparing them to , , and .
How do you compare a fraction to ?
If the numerator is larger than the denominator, the fraction is greater than .
If the numerator is smaller than the denominator, the fraction is smaller than .
In the same way, you can compare fractions to and !
If one fraction is greater than and the other is smaller than , you can determine which fraction is larger without calculating.
Fill in the missing answer:
\( \frac{7}{4}☐\frac{2}{4} \)
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.
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
Solution:
Let's look at the two fractions and notice that is the common denominator.
Since is in the denominator of one of the fractions, we will need to multiply the numerator and denominator of the other fraction - by
We get:
______________
Now, since the denominators are the same, we can just compare the numerators to find out which is greater. Since is greater than , the sign will be .
Another exercise:
Mark the correct sign
Solution:
We can immediately see that it is and that the fractions are identical (any number divided by itself equals ), but we will still follow the method and find a common denominator.
The common denominator will be and we get:
_____________
Now it can be clearly seen that the fractions are identical.
Mark the correct sign
Solution:
Find a common denominator by multiplying the denominators.
Multiply the fraction by , the denominator of the second fraction, and the fraction .
Multiply by , the denominator of the other fraction.
Remember! – Multiply both the numerator and the denominator.
We get:
___________________
Now we compare based on the numerators only. is greater than and therefore the sign is
Another exercise:
Mark the correct sign
_____________________
Solution:
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:
___________________
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
_____________________
Solution:
We will convert the whole number into a fraction - and rewrite the exercise:
Now we will find the common denominator 2 and we get:
_____________________
The fractions are identical, so the sign will be .
Fill in the missing sign:
\( \frac{1}{3}☐\frac{2}{3} \)
Fill in the missing sign:
\( \frac{1}{2}☐\frac{2}{4} \)
Fill in the missing sign:
\( \frac{2}{5}☐\frac{6}{5} \)
Learn the trick:
If the numerators are identical, the larger fraction is the one with the smaller denominator!
Why does this make sense?
Look at the following example:
Dana’s mom made a pizza.
Dana invited Jonathan for dinner, so the pizza was shared equally between Dana and Jonathan.
Each received half a pizza: Dana got , and Jonathan got .
Now, imagine Dana invited Bar and Ofir for dinner as well.
The pizza would need to be shared among four children: Dana, Jonathan, Bar, and Ofir.
The pizza would then be divided into , and each child would get .
Obviously, when more children share the pizza, each person gets less.
The more we divide a whole into pieces, the smaller each piece becomes.
This means that if the numerators are identical but the denominators are different,
the largest fraction will be the one with the smallest denominator.
Exercises:
Mark the correct sign >, <:
_____________
Mark the correct sign >, <:
_____________
Sometimes, you can compare fractions by comparing them to , , and .
If the numerator is larger than the denominator, the fraction is greater than.
If the numerator is smaller than the denominator, the fraction is smaller than .
For the number , the numerator is equal to the denominator.
Therefore, if the numerator and denominator are equal, the fraction equals .
Exercise:
Mark the correct sign >, <:
_____________
Solution:
In the fraction , the numerator is smaller than the denominator. Hence, the fraction is less than .
In the fraction , the numerator is larger than the denominator. Hence, the fraction is greater than .
If one fraction is less than and the other is greater than , the larger fraction is the one greater than .
Exercise:
Mark the correct sign >, <:
_____________
Solution:
In the fraction , the numerator is smaller than the denominator. Hence, the fraction is less than .
In the fraction , the numerator is larger than the denominator. Hence, the fraction is greater than .
Look at the fraction .
In this fraction, the denominator is twice the numerator.
Similarly, any fraction equal to will have a denominator twice as large as the numerator.
Therefore, to compare a fraction to : Multiply the numerator by .
Exercise:
Mark the correct sign >, <:
_____________
Solution:
Look at the fraction .
Multiply the numerator by to get .
is less than the original denominator , so the fraction is less than .
Now look at the fraction .
Multiply the numerator by to get .
is greater than the original denominator , so the fraction is greater than .
If one fraction is less than and the other is greater than , the larger fraction is the one greater than .
Look at the fraction .
In this fraction, the denominator is three times the numerator.
Similarly, any fraction equal to will have a denominator three times as large as the numerator.
Therefore, to compare a fraction to : Multiply the numerator by .
Exercise:
Mark the correct sign >, <:
_____________
Solution:
Look at the fraction .
Multiply the numerator by to get .
is greater than the original denominator , so the fraction is greater than .
Now look at the fraction .
Multiply the numerator by to get .
is less than the original denominator , so the fraction is less than .
Fill in the missing sign:
\( \frac{2}{8}☐\frac{7}{8} \)
Fill in the missing sign:
\( \frac{3}{10}☐\frac{1}{10} \)
Fill in the missing sign:
\( \frac{5}{25}☐\frac{1}{5} \)
Fill in the missing answer:
Let's solve the problem step-by-step:
Both fractions in the problem, and , have the same denominator. This allows us to directly compare their numerators.
The numerators are 7 and 2, respectively. Therefore, we need to determine whether 7 is less than, greater than, or equal to 2.
Comparing 7 and 2:
Since 7 is greater than 2, it follows that:
The correct inequality symbol to fill in the blank is .
Thus, the solution to the problem is .
Therefore, the correct choice from the available options is choice 2: .
>
Fill in the missing sign:
To compare fractions with the same denominator, focus on the numerators:
Therefore, the missing sign that correctly compares the two fractions is , so the correct statement is:
.
>
Fill in the missing sign:
To find the correct comparison sign for the fractions and , follow these logical steps:
Therefore, the missing sign to correctly complete the expression is . Thus, the solution to the problem is .
<
Fill in the missing sign:
To solve the problem, we begin by comparing the fractions and . We will simplify to see if it is equivalent to .
Let's simplify . We do this by finding the greatest common divisor (GCD) of 2 and 4, which is 2. We then divide both the numerator and the denominator by 2:
Now, we see that simplifies to .
Since simplifies to , the two fractions are equivalent.
Therefore, we fill in the missing sign with an equals sign:
Fill in the missing sign:
To solve the problem, we will compare two fractions: and .
Both fractions have the same denominator (8), which allows us to directly compare the numerators. Therefore, we need only consider the values of the numerators to understand the relationship between the two fractions.
Since 2 is less than 7, it follows that is less than .
Therefore, the correct sign to place between and is .
The solution to the problem is .
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