# 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:

### (91/3) : 3 = 28/9 = 3 1/9 ≅ 3.1111111

Spelled result in words is twenty-eight ninths (or three and one ninth).

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

1. Conversion a mixed number 9 1/3 to a improper fraction: 9 1/3 = 9 1/3 = 9 · 3 + 1/3 = 27 + 1/3 = 28/3

To find a new numerator:
a) Multiply the whole number 9 by the denominator 3. Whole number 9 equally 9 * 3/3 = 27/3
b) Add the answer from previous step 27 to the numerator 1. New numerator is 27 + 1 = 28
c) Write a previous answer (new numerator 28) over the denominator 3.

Nine and one third is twenty-eight thirds
2. Divide: 28/3 : 3 = 28/3 · 1/3 = 28 · 1/3 · 3 = 28/9
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 3/1 is 1/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-eight thirds divided by three = twenty-eight ninths.

#### Rules for expressions with fractions:

Fractions - simply use a forward 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 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:

• Fractions 4 How many 2/3s are in 6?
• Unit rate Find unit rate: 6,840 customers in 45 days
• Chocolate Children break chocolate first to third and then every part of another half. What kind got each child? Draw a picture. What part would have received if each piece have halved?
• Women In a company of 1050 employees are 2/3 women. How many women work in the company?
• Find the 11 Find the quotient of 229.12 and 12.32
• 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.
• Container How many three-quarters liters jar fill 30 liters container?
• Minutes Write as fraction in basic form which part of the week is 980 minutes.
• Self A math textbook is 2 2/9 inches thick. How many of these books will fit on a 120-inch self?
• Soup from canteen For how many people is 90 liters of soup enough if we assume 3/8 liter of soup per person in the canteen?
• Evaluate The division of numbers 6 and 3 increase by-product of the numbers 115 and 0.1
• Inheritance After death father (♱ 62) remained mother (his wife) and its 3 children. Inheritance by law is that in the first mother will automatically get half of the property and other one-half inherited by heirs which are mother and her 3 children by the same share
• The third The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod?