What is Fractions Calculators?

Online Fraction calculators are powerful tools designed to perform various operations and conversions involving fractions, decimals, percentages, mixed numbers, and ratios. These calculators use formulas and algorithms to provide accurate results, showing the work involved for better understanding. Below is an explanation of how each calculator works, with examples and formulas.

Fraction Operations and Manipulations

Adding and Subtracting Fractions

Fractions are added or subtracted by finding a common denominator, converting fractions, and performing the operation.
Formula:

 

$$\frac{a}{b} + \frac{c}{d} = \frac{(a \cdot d) + (b \cdot c)}{b \cdot d}$$

 

Example:

 

$$\frac{2}{3} + \frac{3}{4}$$

 

1. LCD of 3 and 4 is 12.
2. Convert fractions:
   $\frac{2}{3} = \frac{8}{12}$

    

   ,

   $\frac{3}{4} = \frac{9}{12}$

    

   .

3. Add:
   $\frac{8}{12} + \frac{9}{12} = \frac{17}{12}$

    

   .
   Result:

   $1 \frac{5}{12}$

    

Mixed Fractions Calculator

Handles operations on mixed numbers by converting them to improper fractions, performing calculations, and converting back to mixed numbers.
Example:

 

$$2 \frac{1}{2} \times 3 \frac{1}{3}$$

 

1. Convert:
   $2 \frac{1}{2} = \frac{5}{2}, 3 \frac{1}{3} = \frac{10}{3}$

    

   .

2. Multiply:
   $\frac{5}{2} \times \frac{10}{3} = \frac{50}{6} = 8 \frac{1}{3}$

    

   .
   Result:

   $8 \frac{1}{3}$

    

Simplifying Fractions Calculator

Reduces fractions to their lowest terms using the GCF.
Formula:

 

$$\frac{a}{b} = \frac{a \div \text{GCF}(a, b)}{b \div \text{GCF}(a, b)}$$

 

Example:

$\frac{18}{24}$

: GCF is 6.

 

$$\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}.$$

 

Result:

$\frac{3}{4}$

 

Simplifying Complex Fractions Calculator

Simplifies fractions where numerators and/or denominators are themselves fractions.
Example:

 

$$\frac{\frac{3}{4}}{\frac{5}{6}}$$

 

1. Multiply by reciprocal:
   $\frac{3}{4} \times \frac{6}{5} = \frac{18}{20}$

    

   .

2. Simplify:
   $\frac{18}{20} = \frac{9}{10}$

    

   .
   Result:

   $\frac{9}{10}$

    

Ratio Calculator

Solves ratio problems using proportional relationships.
Example:
If

$A:B = 3:4$

and

$A = 6$

, find

$B$

.

 

$$\frac{A}{B} = \frac{3}{4}, \quad \frac{6}{B} = \frac{3}{4}.$$

 

Cross-multiply:

$3B = 24 \implies B = 8$

.
Result:

$B = 8$

 

Golden Ratio

Calculates the golden ratio,

$A:B = A+B:A$

.
Formula:

 

$$\frac{A}{B} = \phi \approx 1.618$$

 

Example: If

$A = 5$

, find

$B$

.

 

$$\frac{5}{B} = 1.618 \implies B = \frac{5}{1.618} \approx 3.09.$$

 

Result:

$B \approx 3.09$

 

Solving for X in Fractions

Solves equations involving fractions.
Example:

 

$$\frac{X}{6} = \frac{3}{4}$$

 

Cross-multiply:

$4X = 18 \implies X = 4.5$

.
Result:

$X = 4.5$

 

Converting Fractions, Decimals, and Percents

Decimal to Fraction Converter

Converts decimals to fractions.
Example:
Convert

$0.25$

.

1. Write as
   $\frac{25}{100}$

    

   .

2. Simplify:
   $\frac{25}{100} = \frac{1}{4}$

    

   .
   Result:

   $\frac{1}{4}$

    

Decimal to Percent Converter

Multiplies a decimal by 100 to find the percent.
Example:
Convert

$0.75$

.

 

$$0.75 \times 100 = 75\%.$$

 

Result:

$75\%$

 

Fraction to Decimal Converter

Divides the numerator by the denominator.
Example:
Convert

$\frac{3}{4}$

.

 

$$3 \div 4 = 0.75.$$

 

Result:

$0.75$

 

Fraction to Percent Converter

Converts a fraction to a decimal, then multiplies by 100.
Example:
Convert

$\frac{2}{5}$

.

 

$$\frac{2}{5} = 0.4 \times 100 = 40\%.$$

 

Result:

$40\%$

Percent to Fraction Converter

Converts a percent to a fraction and simplifies.
Example:
Convert

$75\%$

.

 

$$\frac{75}{100} = \frac{3}{4}.$$

 

Result:

$\frac{3}{4}$

 

Mixed Numbers to Improper Fractions

Converts mixed numbers to improper fractions.
Formula:

 

$$\text{Improper Fraction} = \text{Whole} \times \text{Denominator} + \text{Numerator}.$$

 

Example:
Convert

$2 \frac{1}{3}$

.

 

$$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}.$$

 

Result:

$\frac{7}{3}$

 

Improper Fractions to Mixed Numbers

Converts improper fractions to mixed numbers by dividing the numerator by the denominator.
Example:
Convert

$\frac{17}{5}$

.

 

$$17 \div 5 = 3 \text{ remainder } 2.$$

 

Result:

$3 \frac{2}{5}$

.

These calculators simplify complex fraction operations, offering accurate results with step-by-step solutions.