Calculations with Fractions

Fractions are a fundamental part of mathematics, and they are used in many different fields, from science and engineering to finance and economics.

Understanding how to perform calculations with fractions is essential for solving many math problems, and it is a skill that can be applied in many areas of life.

In this article, we will explore the basics of calculations with fractions, including adding, subtracting, multiplying, and dividing them.

Whether you are a student learning about fractions for the first time or an adult looking to brush up on your math skills, this guide will provide you with the knowledge you need to confidently work with fractions. 

How to Calculate Fractions

There are many calculations you can perform with fractions, including adding, subtracting, multiplying, and dividing. Here are some step-by-step instructions for each operation:

1. Adding fractions

To add fractions, you need to find a common denominator (a number that both denominators can divide into evenly) and then add the numerators together. Here are the steps:

• Find a common denominator: If the denominators are already the same, skip this step. If not, find the least common multiple (LCM) of the two denominators, and then rewrite each fraction so that they have the same denominator.
• Add the numerators: Once the fractions have the same denominator, add the numerators together, and write the result over the common denominator. Simplify the fraction if necessary.

For example:

1/3 + 1/4 = 4/12 + 3/12 = 7/12

2. Subtracting fractions

Subtracting fractions is similar to adding them, but instead of adding the numerators, you subtract them. Here are the steps:

• Find a common denominator: If the denominators are already the same, skip this step. If not, find the LCM of the two denominators, and then rewrite each fraction so that they have the same denominator.
• Subtract the numerators: Once the fractions have the same denominator, subtract the numerators, and write the result over the common denominator. Simplify the fraction if necessary.

For example:

1/2 - 1/3 = 3/6 - 2/6 = 1/6

3. Multiplying fractions

To multiply fractions, you simply multiply the numerators together and then multiply the denominators together. Here are the steps:

• Multiply the numerators: Multiply the numerators together.
• Multiply the denominators: Multiply the denominators together.
• Simplify the result if necessary.

For example:

2/3 * 3/4 = (23) / (34) = 6/12 = 1/2

4. Dividing fractions

To divide fractions, you invert (flip) the second fraction and then multiply the first fraction by the inverted second fraction. Here are the steps:

• Invert the second fraction: Flip the second fraction over so that the numerator becomes the denominator, and the denominator becomes the numerator.
• Multiply the fractions: Multiply the first fraction by the inverted second fraction.
• Simplify the result if necessary.

For example:

2/3 ÷ 3/4 = 2/3 * 4/3 = (24) / (33) = 8/9

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