Fraction Calculator: Definition, Formula, Examples, and FAQ

Published: 4/26/2021 Last updated: 2/23/2023

Table of contents:

Definition of Fraction Calculator
Formula for Fraction Calculator
Examples of Fraction Calculator
Question and Answer FAQ
What is a fraction calculator?
How do I use a fraction calculator?
What are some common applications of fraction calculators?
Are there any limitations to using a fraction calculator?
Conclusion

Fractions are a fundamental concept in mathematics that are used to represent part of a whole. A fraction is a way of expressing a number as a ratio of two integers, where the top number is called the numerator and the bottom number is called the denominator. Fractions are used in a wide range of mathematical and real-world applications, from basic arithmetic operations to complex algebraic equations. In this article, we will discuss the fraction calculator, its definition, formula, examples, and frequently asked questions.

Definition of Fraction Calculator

A fraction calculator is a tool that helps you perform arithmetic operations with fractions, including addition, subtraction, multiplication, and division. It is a useful tool for students and professionals who work with fractions on a regular basis. Fraction calculators are available in both physical and digital forms, including handheld calculators, online calculators, and mobile apps. They can be used to perform a wide range of mathematical operations, from basic calculations to complex equations.

Formula for Fraction Calculator

The formula for a fraction calculator depends on the operation being performed. Here are the formulas for the four basic arithmetic operations:

Addition: To add two fractions, you need to find a common denominator, then add the numerators together. The result is a fraction with the same denominator as the original fractions. The formula is as follows:

$\frac{a}{b}+\frac{c}{d} = \frac{ad + bc}{bd}$

Subtraction: To subtract two fractions, you need to find a common denominator, then subtract the numerators. The result is a fraction with the same denominator as the original fractions. The formula is as follows:

$\frac{a}{b}-\frac{c}{d} = \frac{ad - bc}{bd}$

Multiplication: To multiply two fractions, you simply multiply the numerators together, then multiply the denominators together. The formula is as follows:

$\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$

Division: To divide two fractions, you need to invert the second fraction, then multiply the two fractions together. The formula is as follows:

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}$

Examples of Fraction Calculator

Let's take a look at some examples of how to use a fraction calculator to perform arithmetic operations with fractions.

Example 1: Add 2/3 and 5/6.

$\frac{2}{3}+\frac{5}{6} = \frac{4}{6}+\frac{5}{6} = \frac{9}{6}$

We can simplify the result by dividing both the numerator and denominator by their greatest common factor (GCF), which is 3.

$\frac{9}{6} = \frac{3\cdot 3}{2\cdot 3} = \frac{3}{2}$

Therefore, 2/3 + 5/6 = 3/2. Example 2: Subtract 3/5 from 7/8.

$\frac{7}{8}-\frac{3}{5} = \frac{35}{40}-\frac{24}{40} = \frac{11}{40}$

Therefore, 7/8 - 3/5 = 11/40. Example 3: Multiply 2/3 by 4/5.

$\frac{2}{3} \cdot \frac{4}{5} = \frac{2\cdot 4}{3\cdot 5} = \frac{8}{15}$

Therefore, 2/3 x 4/5 = 8/15. Example 4: Divide 3/4 by 1/2.

$\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \cdot \frac{2}{1} = \frac{6}{4}$

We can simplify the result by dividing both the numerator and denominator by their GCF, which is 2.

$\frac{6}{4} = \frac{3\cdot 2}{2\cdot 2} = \frac{3}{2}$

Therefore, 3/4 ÷ 1/2 = 3/2.

Question and Answer FAQ

What is a fraction calculator?

A fraction calculator is a tool that allows you to perform arithmetic operations with fractions, such as addition, subtraction, multiplication, and division. It takes two or more fractions as inputs and produces a fraction as the output.

How do I use a fraction calculator?

Using a fraction calculator is easy. Simply enter the fractions you want to perform an arithmetic operation with and select the operation you want to perform. The calculator will then display the result of the operation in the form of a fraction.

What are some common applications of fraction calculators?

Fraction calculators are commonly used in many fields, including math, science, engineering, and finance. They are particularly useful in situations where fractions are involved, such as calculating proportions, percentages, and ratios.

Are there any limitations to using a fraction calculator?

While fraction calculators are a helpful tool, they do have some limitations. They may not be able to handle extremely large or small fractions, and they may not be able to simplify fractions as much as possible. Additionally, they may not be able to perform some more complex operations involving fractions, such as finding the least common denominator or converting between mixed numbers and improper fractions.

Conclusion

A fraction calculator is a valuable tool for performing arithmetic operations with fractions. It simplifies the process of performing calculations with fractions and reduces the likelihood of errors. By using a fraction calculator, you can save time and effort in performing mathematical operations involving fractions. However, it is important to keep in mind that fraction calculators may have some limitations and may not be able to handle all types of fraction-related problems.