# 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:

### 81/8 - 43/8 = 15/4 = 3 3/4 = 3.75

Spelled result in words is fifteen quarters (or three and three quarters).

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

1. Conversion a mixed number 8 1/8 to a improper fraction: 8 1/8 = 8 1/8 = 8 · 8 + 1/8 = 64 + 1/8 = 65/8

To find new numerator:
a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8
b) Add the answer from previous step 64 to the numerator 1. New numerator is 64 + 1 = 65
c) Write a previous answer (new numerator 65) over the denominator 8.

Eight and one eighth is sixty-five eighths
2. Conversion a mixed number 4 3/8 to a improper fraction: 4 3/8 = 4 3/8 = 4 · 8 + 3/8 = 32 + 3/8 = 35/8

To find new numerator:
a) Multiply the whole number 4 by the denominator 8. Whole number 4 equally 4 * 8/8 = 32/8
b) Add the answer from previous step 32 to the numerator 3. New numerator is 32 + 3 = 35
c) Write a previous answer (new numerator 35) over the denominator 8.

Four and three eighths is thirty-five eighths
3. Subtract: 65/8 - 35/8 = 65 - 35/8 = 30/8 = 2 · 15/2 · 4 = 15/4
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(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the next intermediate step , cancel by a common factor of 2 gives 15/4.
In words - sixty-five eighths minus thirty-five eighths = fifteen quarters.

#### 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?