# 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:

### 2/3 / 6 = 1/9 ≅ 0.1111111

Spelled result in words is one ninth.

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

1. Divide: 2/3 : 6 = 2/3 · 1/6 = 2 · 1/3 · 6 = 2/18 = 2 · 1 /2 · 9 = 1/9
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 6/1 is 1/6) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 1/9.
In words - two thirds divided by six = one ninth.

#### 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:

• A quotient
What is the quotient of 3/10 divided by 2/4 as a fraction?
• Fraction of a fraction
What is two-quarters of twelve?
• Monica 3
Monica works on her drawings for 2 hours. She spends 1/6 hour on each drawing. How many drawings does she work on in 2 hours?
• Day
What part of the day are 23 hours 22 minutes? Express as a decimal number.
• Pediatrician
Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work?
• The bird
The bird feeder holds 1 and 1/2 cups of birdseed. Reagan is using a scoop that holds 1/8 of a cup. How many scoops will she need to fill the bird feeder?
• 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?
• Volume per time 2
Benjamin drinks tea at an incredible rate. He drinks 3 1/2 liters of tea every 2/3 of an hour. Ben drinks tea at a constant rate. How much does he drink in one hour?
• How many 14
How many 1/2 cup serving are in a package of cheese that contains 5 1/4 cups altogether?
• TV fail
The TV has after 10,000 hours average 35 failures. Determine the probability of TV failure after 400 hours of operation.
• Jerry
Jerry has 3/4 of a pizza. He needs to share it with 6 friends. What fraction of the pizza will each friend get? Only write the fraction
• 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?
• Rope cutting
Shane has a piece of rope that is 7 4/5 units long. If he cuts it into pieces that are each 3/5 of a unit long, how many pieces does he have?