समान और असमान भिन्न

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There are two broad categories of fractions based on their denominators. You can add, subtract or compare fractions only if they are like fractions. If the fractions are unlike fractions, they need to be converted to like fractions before adding, subtracting, or comparing.

Let’s find out what are like and unlike fractions and how they differ from one another.

What are Like and Unlike Fractions?

Whenever you write two or more fractions, then those fractions can be grouped as like fractions or unlike fractions. The difference between these two fractions lies in the denominators of the fractions in a group of fractions. For example $\frac {1}{4}$ and $\frac {3}{4}$ are like fractions, whereas $\frac {3}{4}$ and $\frac {5}{7}$ are unlike fractions.

Like Fractions

The fractions which have the same denominator are called like fractions. i.e. their denominators are equal. For example, fractions in a group such as $\frac {1}{8}$, $\frac {2}{8}$ $\frac {3}{8}$, $\frac {4}{8}$, $\frac {5}{8}$ are like fractions. Since the denominators of each of the fractions are the same i.e. 8, they are like fractions. In like fractions, the whole is always the same which is represented by the common denominators.

Note:

  • The fractions such as $\frac {1}{4}$, $\frac {2}{8}$, $\frac {3}{12}$ and $\frac {4}{16}$ are also called like fractions because they are all equivalent to fraction $\frac {1}{4}$. These fractions after simplifying will all have the denominator $4$.
  • Whole numbers such as $1$, $2$, $3$, and so on are considered like fractions since all these numbers can also be written as $\frac {1}{1}$, $\frac {2}{1}$, $\frac {3}{1}$, and so on.

Unlike Fractions

The fractions which have different denominators are called unlike fractions, i.e. their denominators are not equal. For example, fractions in a group such as $\frac {1}{8}$, $\frac {1}{7}$ $\frac {3}{11}$, $\frac {5}{19}$, and $\frac {9}{23}$ are unlike fractions. Since the denominators of each of the fractions are different, they are unlike fractions. In the case of unlike fractions, the wholes are different and are represented by their denominators.

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Why Knowing the Difference Between Like Fractions and Unlike Fractions Necessary?

When adding or subtracting fractions, we must be knowing the difference between like fractions and unlike fractions.

Adding or subtracting two or more like fractions is always easier as they can be added or subtracted directly without any manipulation or simplification. But when you want to add or subtract two or more unlike fractions, you have to use either the cross-multiplication method or the LCM (Least common multiple) methods to add or subtract two or more fractions.

Converting Unlike Fractions to Like Fractions

As mentioned above you can add or subtract fractions only when the fractions have the same denominators or when the fractions are like fractions, therefore it becomes necessary to know the process of converting unlike fractions to like fractions.

Steps to Convert Unlike Fractions to Like Fractions

The steps to convert unlike fractions to like fractions following steps are used.

Step 1: Find the LCM of the denominators of the fractions

Step 2: Multiply the numerator and denominator of each fraction by a number such that the denominator becomes equal to the LCM

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उदाहरण

Ex 1: Convert the fractions to like fractions – $\frac {1}{2}$, $\frac {2}{3}$, $\frac {3}{5}$, and $\frac {4}{7}$.

The denominators in the fractions are $2$, $3$, $5$, and $7$.

LCM of $2$, $3$, $5$ and $7$ is $210$.

Now get numbers to multiply the corresponding numerators.

$210 \div 2 = 105$, $210 \div 3 = 70$, $210 \div 5 = 42$, and $210 \div 7 = 30$.

Multiplying the numerator and the denominator of each fraction by $105$, $70$, $42$, and $30$ respectively.

$\frac {1 \times 105}{2 \times 105} = \frac {105}{210}$

$\frac {2 \times 70}{3 \times 70} = \frac {140}{210}$

$\frac {3 \times 42}{5 \times 42} = \frac {126}{210}$

$\frac {4 \times 30}{7 \times 30} = \frac {120}{210}$

$\frac {105}{210}$, $\frac {140}{210}$, $\frac {126}{210}$, and $\frac {120}{210}$ are like fractions corresponding to the fractions $\frac {1}{2}$, $\frac {2}{3}$, $\frac {3}{5}$, and $\frac {4}{7}$.

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Arithmetic Operations With Like and Unlike Fractions

There are four basic arithmetic operations

  • Addition
  • Subtraction
  • Multiplication
  • विभाजन

Each of these operations can be performed on like and unlike fractions.

Addition and Subtraction of Like and Unlike Fractions

The process for adding and subtracting fractions with like denominators is quite simple because we just need to add or subtract the numerators keeping the denominator the same.

To add or subtract unlike fractions, first of all, the denominators are made equal and converted to like fractions. After that, we use the steps of addition or subtraction of like fractions.

To know more about adding like and unlike fractions, click here.

Multiplication and Division of Like and Unlike Fractions

The process of multiplication and division of like and unlike fractions is the same as in the case of multiplication and division of fractions, the condition that denominators should be the same is not required.

In the case of multiplication, the numerator of one fraction is multiplied with the numerator of the other fraction and similarly, the denominator of one fraction is multiplied with the denominator of the other fraction.

In the case of division, first of all, the reciprocal of the second fraction is taken and then multiplied with the first fraction.

To know more about adding like and unlike fractions, click here.

निष्कर्ष

समान और असमान भिन्न भिन्नों की दो व्यापक श्रेणियां हैं। Two or more fractions are called like fractions when their denominators are the same, whereas, in the case of unlike fractions, the denominators of the fractions are different. Certain operations like addition, subtraction, and comparison can be performed only with like fractions. In such cases, the first step is to convert the fractions to like fractions, if they are not.

Practice Problems

  1. Which of the following are like fractions?
    • $\frac {2}{3}$, $\frac {6}{11}$, $\frac {5}{7}$, $\frac {1}{3}$, $\frac {11}{13}$, $\frac {2}{11}$, $\frac {9}{13}$, $\frac {5}{7}$, $\frac {6}{11}$, $\frac {5}{13}$
    • $\frac {1}{2}$, $\frac {3}{7}$, $\frac {5}{7}$, $\frac {9}{23}$, $\frac {15}{19}$, $\frac {5}{23}$, $\frac {6}{7}$, $\frac {15}{23}$
  2. Convert the following fractions into like fractions
    • $\frac {1}{2}$, $\frac {1}{3}$, $\frac {1}{4}$, $\frac {1}{5}$, $\frac {1}{6}$
    • $\frac {2}{3}$, $\frac {2}{5}$, $\frac {3}{4}$, $\frac {1}{2}$, $\frac {12}{15}$, $\frac {17}{30}$

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