Fraction Calculator

What is a Fraction?

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It consists of two numbers separated by a horizontal or diagonal line, where the number above the line is called the numerator, and the number below the line is called the denominator.

In a fraction, the numerator represents the number of equal parts you have or are interested in, while the denominator represents the total number of equal parts that make up the whole.

For example, in the fraction 3/4:

• The numerator (3) represents that you have three parts out of the total.
• The denominator (4) represents that the whole is divided into four equal parts.

So, 3/4 indicates that you have three out of four equal parts or three-quarters of the whole.

Fractions can represent various quantities and can be used for a wide range of purposes in mathematics and everyday life, such as measuring, comparing, and calculating proportions. They are essential in areas like arithmetic, algebra, geometry, and science for expressing values that are not whole numbers or integers.

Converting between fractions and decimals

Converting between fractions and decimals involves expressing a given value in either fractional form (a ratio of two integers) or decimal form (a numerical representation with a decimal point). I'll provide instructions for both conversions:

1. Converting Fractions to Decimals:
   • To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number).
   • Perform the division and express the result as a decimal.
   • For example, to convert the fraction 3/4 to a decimal: Divide 3 by 4: 3 ÷ 4 = 0.75. So, 3/4 as a decimal is 0.75.
2. Converting Decimals to Fractions:
   • Write the decimal number as a fraction with the decimal part as the numerator and a power of 10 as the denominator.
   • Simplify the fraction if possible.
   • For example, to convert the decimal 0.625 to a fraction: Write it as a fraction: 0.625 = 625/1000. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (in this case, 125): (625/1000) ÷ (125/125) = 5/8. So, 0.625 as a fraction is 5/8.

Keep in mind that not all decimals can be expressed as simple fractions. Some decimals are recurring (repeating) or non-terminating (never-ending), and they are typically represented as repeating decimals or approximated using the symbol "≈."

For example, the decimal 1.333... (with an infinite number of 3s) is equivalent to the fraction 4/3, and the decimal π (pi) is approximately 3.14159 and cannot be expressed as a finite fraction.

Adding fractions example

Subtracting fractions example

Multiplying fractions example

Dividing fractions example