# Fraction calculator

The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

## Result:

### 31/4 - 21/3 = 11/12 ≅ 0.9166667

Spelled result in words is eleven twelfths.

### How do you solve fractions step by step?

1. Conversion a mixed number 3 1/4 to a improper fraction: 3 1/4 = 3 1/4 = 3 · 4 + 1/4 = 12 + 1/4 = 13/4

To find new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 4.

Three and one quarter is thirteen quarters
2. Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

To find new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds
3. Subtract: 13/4 - 7/3 = 13 · 3/4 · 3 - 7 · 4/3 · 4 = 39/12 - 28/12 = 39 - 28/12 = 11/12
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(4, 3) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 3 = 12. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - thirteen quarters minus seven thirds = eleven twelfths.

#### Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2

#### Examples:

subtracting fractions: 2/3 - 1/2
multiplying fractions: 7/8 * 3/9
dividing Fractions: 1/2 : 3/4
exponentiation of fraction: 3/5^3
fractional exponents: 16 ^ 1/2
adding fractions and mixed numbers: 8/5 + 6 2/7
dividing integer and fraction: 5 ÷ 1/2
complex fractions: 5/8 : 2 2/3
decimal to fraction: 0.625
Fraction to Decimal: 1/4
Fraction to Percent: 1/8 %
comparing fractions: 1/4 2/3
multiplying a fraction by a whole number: 6 * 3/4
square root of a fraction: sqrt(1/16)
reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
expression with brackets: 1/3 * (1/2 - 3 3/8)
compound fraction: 3/4 of 5/7
fractions multiple: 2/3 of 3/5
divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

What is 4 1/2+2/7-213/14?
• Length subtracting
Express in mm: 5 3/10 cm - 2/5 mm
• Difference mixed fractions
What is the difference between 4 2/3 and 3 1/6?
• School
There are 150 pupils in grade 5 . 2/3 of it are female. By what fractions are the males?
• Pizza fractions
Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
• Cake fractions
Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
• Mixed numbers
Rewrite mixed numbers so the fractions have the same denominator: 5 1/5 - 2 2/3
• Pounds
3 pounds subtract 1/3 of a pound.
• From a
From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece?
• King
King had four sons. First inherit 1/2, second 1/4 , third 1/5 of property. What part of the property was left to the last of the brothers?
• Erica
Erica bought 3 1/2 yards of fabric. If she uses 2/3 of the fabric, how much will she have left?
• Employees
Of all 360 employees, there are 11/12 women. How many men work in a company?
• Savings
Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?