Fraction Calculator
A fraction calculator performs calculations with fractions, including addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. It is useful for everyday calculations, school mathematics, algebra, measurements, and other situations involving fractional values.
What Is a Fraction?
A fraction represents a part of a whole and is written with a numerator above a denominator:
a/b
The numerator is the top number, while the denominator is the bottom number. The denominator cannot be zero.
Adding and Subtracting Fractions
Fractions with the same denominator can be added or subtracted by keeping the denominator and operating on the numerators.
For example:
2/7 + 3/7 = 5/7
When the denominators are different, first find a common denominator.
For example:
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Multiplying Fractions
To multiply fractions, multiply the numerators together and multiply the denominators together:
(2/3) Γ (5/7) = 10/21
The result can then be simplified if the numerator and denominator have a common factor.
Dividing Fractions
To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction.
For example:
(3/4) Γ· (2/5) = (3/4) Γ (5/2) = 15/8
This can also be written as the mixed number 1 7/8.
Simplifying Fractions
A fraction is in simplest form when the numerator and denominator have no common factor greater than 1.
For example:
12/18 = 2/3
Both 12 and 18 can be divided by their greatest common factor, 6.
Mixed Numbers and Improper Fractions
A mixed number contains a whole number and a proper fraction, such as 2 1/3.
An improper fraction has a numerator greater than or equal to its denominator, such as 7/3.
To convert 2 1/3 to an improper fraction:
(2 Γ 3 + 1) Γ· 3 = 7/3
Fraction and Decimal Conversion
To convert a fraction to a decimal, divide the numerator by the denominator.
For example:
3/4 = 3 Γ· 4 = 0.75
To convert a terminating decimal to a fraction, write it over the appropriate power of 10 and simplify.
For example:
0.6 = 6/10 = 3/5
Common Fraction Calculations
| Calculation | Result |
|---|---|
| 1/2 + 1/4 | 3/4 |
| 3/4 β 1/4 | 1/2 |
| 2/3 Γ 3/5 | 2/5 |
| 3/5 Γ· 2/3 | 9/10 |
| 12/18 simplified | 2/3 |
Common Mistakes to Avoid
Do not add or subtract denominators directly. For addition and subtraction, fractions need a common denominator first.
When dividing fractions, remember to invert the second fraction before multiplying. Also check that the denominator of the final fraction is not zero.
Quick Summary
A fraction calculator can add, subtract, multiply, divide, simplify, and convert fractions. For accurate results, use a common denominator for addition and subtraction, multiply numerators and denominators for multiplication, and use the reciprocal when dividing.