# 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:

### (1/3) : (1/11) = 11/3 = 3 2/3 ≅ 3.6666667

Spelled result in words is eleven thirds (or three and two thirds).

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

1. Divide: 1/3 : 1/11 = 1/3 · 11/1 = 1 · 11/3 · 1 = 11/3
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/11 is 11/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one third divided by one eleventh = eleven thirds.

#### 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:

• Women
In a company of 1050 employees are 2/3 women. How many women work in the company?
• Division of money
Calculate how many euros have Matthew, Miriam, Lucy, Michael, Janka when together have 2,700 euros and the amounts are at a ratio of 1:5:6:7:8.
• Reminder and quotient
There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
• Tape
Video is 153% more expensive than tape recorder. How many percent is tape recorder less expensive than video?
• A quotient
What is the quotient of 3/10 divided by 2/4 as a fraction?
• Product of two fractions
Product of two fractions is 9 3/5 . If one of the fraction is 9 3/7. Find the other fraction.
• Fraction expression
Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
• Quotient and division
What is the quotient of 2/9 and 1/8?
• A PVC pipe
A PVC pipe 12 feet long is to be cut into 1 1/2 foot pieces.  How many pieces can a plumber get out of this length pipe?
• Reciprocal value 2
Annabelle is making burger patties if each burger patty needs 1/16 kilogram of beef. How many patties can she make with a kilo of beef?
• Split between 4
There are 12 1/4 pounds of candy canes to split between four classes evenly. How many pounds of the candy canes will each class get?
• Quotient 3
If the quotient of 8/13 and 2 is subtracted from the product of 1 3/4 and 8/21, what is the difference?
• Fraction to decimal infinite
Determine which digit is at 1000th place after the decimal point in the decimal expansion of the fraction 9/28.