## Like and Unlike Fractions

Fractions are in the form of \[\frac{p}{q}\] where q is not equal to zero. It has two parts. P is called the numerator and the second one is q which is called the denominator. Like and unlike fractions are the most common topic in a lower grade. Have we ever thought about what is like fraction and unlike fraction? These are basically the comparison between two fractions. Depending on the denominator they are segregated into like and unlike fractions. Apart from that, we’ll also see adding fractions with unlike denominators examples later.

### Like Fraction Definition:

It is also called denominators. When two fractions are compared and they have the same denominator, then we say given fractions are like fractions. It is also called denominators.

For example: consider two fractions \[\frac{2}{5}\] and \[\frac{7}{5}\]. Observe that, they have numerators as 2 and 7. On the other hand, denominators of the given fractions are the same which is 5. Hence, they are like fractions or like denominators because of the same denominators.

### Unlike Fraction Definition:

What is unlike fraction definition? Simply, When two fractions are compared and they have a different denominator, then we say given fractions are unlike fractions. In other words, fractions having different denominators are called, unlike fractions. It is also called, unlike denominators.

For example: consider two fractions \[\frac{2}{3}\] and \[\frac{5}{7}\]. Observe that, they have numerators as 2 and 5. On the other hand denominators of the given fractions are 3 and 7. Hence, they are like fractions or like denominators because of different denominators.

### How to Convert Unlike Fractions to Like Fractions?

It is difficult to compare or perform operations like addition and subtraction of fractions of unlike denominators. To do so, it is necessary for us to convert unlike the denominator fraction to like-kind. To make the same denominator least common multiple which is also known as LCM plays a vital role.

Let us suppose we want to compare fractions \[\frac{3}{4}\] and \[\frac{5}{7}\]. Observe that, we can not compare them as they have different denominators. We’ll take LCM of denominators 4 and 7. Since these two are co-prime numbers that are relatively prime numbers, their least common multiple will be nothing but the product of these two. Now the product of 4 and 7 will be 28. After equating the denominator, we’ll compare the numerators and tell which one is bigger than the other.

\[\frac{3}{4}\] , \[\frac{5}{7}\]

On taking LCM

\[\frac{21, 20}{28}\]

⇒ \[\frac{21}{28}\], \[\frac{20}{28}\]

Since 21 is bigger than 20 so \[\frac{3}{4}\] is bigger than \[\frac{5}{7}\].

### Adding Fractions with Unlike Denominator Example

Let us suppose, we want to add fractions \[\frac{3}{4}\] and \[\frac{5}{7}\]. As we discussed earlier, it is not possible at all operating fractions with unlike denominators. First, we’ll take the least common multiple to convert given unlike denominators into like denominators then we’ll add them.

\[\frac{3}{4}\] + \[\frac{5}{7}\]

⇒ \[\frac{3 \times 7 + 5 \times 4}{28}\]

⇒ \[\frac{21 + 20}{28}\]

⇒ \[\frac{41}{28}\]

### Subtracting Fractions with Unlike Denominator Example

Subtractions are similar to addition. The only difference is that in addition, we used to add numerators in the end after equating denominators whereas in subtraction we’ll subtract them.

Let us suppose we want to subtract \[\frac{3}{4}\] from \[\frac{5}{7}\]. Then

\[\frac{5}{7}\] - \[\frac{3}{4}\]

⇒ \[\frac{5 \times 4 - 3 \times 7}{7 \times 4}\]

⇒ \[\frac{20 - 21}{28}\]

⇒ \[\frac{-1}{28}\]

### Did You Know?

We can actually compare fractions with unlike denominators and like numerators. The fraction will always be greater which has a smaller denominator.

For example: If we compare fractions 115and 117, then 115 will be greater than 117 because 5 is less than 7.

It is not necessary to take the least common multiple of denominators for addition or subtracting fraction, unlike denominators. Any common multiple will do the job. Nonetheless, prefer the least common multiple of denominator because it’ll reduce the workload of calculation.

Multiplication and division of fractions can be computed as usual. In these operations, we don’t need to make the denominator the same.

Question: How Do We Add Fractions with Unlike Denominators?

Answer: The fractions with different denominators are often added by making the denominators common. This is possible by multiplying the numerator and denominator of each of the fractions with an appropriate constant. To add the fractions 3/5 + 4/3, we'd like to multiply both the fractions with such a number which makes the denominators equal. For this, we'd like the LCM of the denominators, which is 15 in this case. The numerator and denominator of the primary fraction 3/5 are multiplied by 3, and therefore the numerator and denominator of the second fraction 4/3 is multiplied by 5. Hence, we have

(3/5 × 3/3) + (4/3 × 5/5)

= (9/15) + (20/15)

= (9 + 20)/15

= 29/15

Question: How Do We Add Three Fractions with Different Denominators?

Answer: The addition of three fractions is the same as the addition of two fractions with different denominators. First of all, we need the LCM of all three denominators. Accordingly, the denominators of all the three fractions are made common by multiplying the numerator and denominator of every one of the fractions with an appropriate number. Now, once the denominators are common, the numerators are added to urge the sum of the fraction. Let us understand this with the assistance of this additional problem:

2/3 + 4/5 + 1/6.

The LCM of 3, 5, 6 is 30. Now, we will multiply each fraction with the suitable number to make their denominators common:

(2/3 × 10/10) + (4/5 × 6/6) + (1/6 × 5/5)

= (20/30) + (24/30) + (5/30)

= (20 + 24 + 5)/30

= 49/30

Question: What is Unlike Fraction with Example?

Answer: fraction having a different denominator is called, unlike fractions. For example, 5/8 and 11/5 are unlike fractions because they have a different denominator.