How to Convert Unlike Fractions into Like Fractions

Converting unlike fractions into like fractions is an essential skill in mathematics, particularly in operations such as addition and subtraction. By converting fractions into like fractions, we can easily perform these operations and compare fractions effectively. In this guide, we will explain the process of converting unlike fractions into like fractions in detail.

Understanding Unlike Fractions

Unlike fractions are fractions that have different denominators. For example, 1/5 and 2/7 are unlike fractions because they have different denominators (5 and 7, respectively). Unlike fractions cannot be directly added, subtracted, or compared. Therefore, it is necessary to convert them into like fractions before performing any operations.

Steps to Convert Unlike Fractions into Like Fractions

To convert unlike fractions into like fractions, we need to find a common denominator. A common denominator is a number that is divisible by both denominators of the given fractions. Here are the steps to convert unlike fractions into like fractions:

1. Identify the denominators: Take note of the denominators of the given fractions.

2. Find the least common multiple (LCM): Determine the least common multiple of the denominators. The LCM is the smallest number that is divisible by both denominators. There are various methods to find the LCM, such as prime factorization, listing multiples, or using a common multiple table.

3. Convert the fractions: Multiply the numerator and denominator of each fraction by the same value that will make the denominator equal to the LCM. This will result in fractions with the same denominator, making them like fractions.

4. Simplify (if necessary): Once the fractions have the same denominator, you can perform operations like addition or subtraction. If needed, simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Example:

Let's convert the unlike fractions 1/5 and 2/7 into like fractions.

1. The denominators are 5 and 7.

2. The LCM of 5 and 7 is 35.

3. To convert 1/5 into a fraction with a denominator of 35, we multiply both the numerator and denominator by 7: (1/5) * (7/7) = 7/35.

Similarly, to convert 2/7 into a fraction with a denominator of 35, we multiply both the numerator and denominator by 5: (2/7) * (5/5) = 10/35.

4. The converted like fractions are 7/35 and 10/35. If needed, we can simplify them further by dividing the numerator and denominator by their GCD.

By following these steps, you can convert unlike fractions into like fractions, enabling you to perform operations and comparisons efficiently. Practice these steps with different examples to enhance your understanding and proficiency in converting unlike fractions.