# 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:

### 356/34 - 51/2 = -29/34 ≅ -0.8529412

Spelled result in words is minus twenty-nine thirty-fourths.

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

1. Conversion a mixed number 3 56/34 to a improper fraction: 3 56/34 = 3 56/34 = 3 · 34 + 56/34 = 102 + 56/34 = 158/34

To find new numerator:
a) Multiply the whole number 3 by the denominator 34. Whole number 3 equally 3 * 34/34 = 102/34
b) Add the answer from previous step 102 to the numerator 56. New numerator is 102 + 56 = 158
c) Write a previous answer (new numerator 158) over the denominator 34.

Three and fifty-six thirty-fourths is one hundred fifty-eight thirty-fourths
2. Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2

To find new numerator:
a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2
b) Add the answer from previous step 10 to the numerator 1. New numerator is 10 + 1 = 11
c) Write a previous answer (new numerator 11) over the denominator 2.

Five and one half is eleven halfs
3. Subtract: 158/34 - 11/2 = 158/34 - 11 · 17/2 · 17 = 158/34 - 187/34 = 158 - 187/34 = -29/34
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(34, 2) = 34. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 34 × 2 = 68. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - one hundred fifty-eight thirty-fourths minus eleven halfs = minus twenty-nine thirty-fourths.

#### 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?
• 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?
• Pounds
3 pounds subtract 1/3 of a pound.
• Employees
Of all 360 employees, there are 11/12 women. How many men work in a company?
• Package
The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
• Akpan
Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week?
• A jewelry
A jewelry store has 20 grams of gold. If a pair of earrings need 1/4 gram of gold, how many grams are not used?
• Regrouping
Subtract mixed number with regrouping: 11 17/20- 6 19/20
• Mixed numbers
Rewrite mixed numbers so the fractions have the same denominator: 5 1/5 - 2 2/3
• A laundry
Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?