# 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:

### 3.875 = 31/8 = 3 7/8

Spelled result in words is thirty-one eighths (or three and seven eighths).

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

1. Conversion a decimal number to a fraction: 3.875 = 3875/1000 = 31/8

a) Write down the decimal 3.875 divided by 1: 3.875 = 3.875/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
3.875/1 = 38.75/10 = 387.5/100 = 3875/1000
Note: 3875/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
3875/1000 = 31 * 125/8 * 125 = 31 * 125/8 * 125 = 31/8

#### 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:

• Zdeněk
Zdeněk picked up 15 l of water from a 100-liter full-water barrel. Write a fraction of what part of Zdeněk's water he picked.
• Lowest terms 2
The expression 4/12 can be expressed in its lowest term as 1/3. What is 3/15 expressed in its lowest term?
• Students
There are 1100 students at a school. 540 students are girls, the rest are boys. 1/10 of girls are left handed. 1/8 of the boys are left handed. Work out the number of left handed students in the school.
• Report 2
A School reports students to teacher ratio of 6:1. If there are 45 teachers in the School, how many students are there?
• Simplify 9
Simplify and express the result as a rational number in its simplest form 1/2+ 1/5+ 6.25+0.25
• Number
I think the number. If I add to its third seven I get same as when to its quarter add 8. Which is the number?
• A market
A market vendor was able to sell all the mangoes, papayas, and star apples.  1/5  of the fruits were mangoes,   2/3  of them were papayas and the rest were star apples.  How many parts of the fruits sold are star apples?
• Golf balls
Of the 28 golf balls, 1/7 are yellow. How many golf balls are yellow? Use the model to help you. Enter your answer in the box.
• Blue silk
There are 4 rolls of blue silk. Each roll holds 6 3/4 yd of silk. It takes 3/5 of a yard to make one necktie. How many necktie can be made from the 4 rolls of blue silk?
• Seed germination
Seed germination is 80%. 8% of the germinated plants subsequently die. How many seeds does a gardener have to sow in order to grow 2,000 plants?