# 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:

### 8/9 - 1/2 = 7/18 ≅ 0.3888889

Spelled result in words is seven eighteenths.

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

1. Subtract: 8/9 - 1/2 = 8 · 2/9 · 2 - 1 · 9/2 · 9 = 16/18 - 9/18 = 16 - 9/18 = 7/18
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 both denominators - LCM(9, 2) = 18. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 2 = 18. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - eight ninths minus one half = seven eighteenths.

#### 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:

• Pears
There were pears in the basket, I took two-fifths of them, and left six in the basket. How many pears did I take?
• UN 1
If we add to an unknown number his quarter, we get 210. Identify unknown number.
Shade the area on the grid that shows 5/8 x 2/4
• Fruits
Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all?
• Trees
3/5 trees are apples, cherries are 1/3. 5 trees are pear. How many is the total number of trees?
• 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?
• The tap
For one day flows 148 l of water out of the tap. How much water will flow out for 3/4 day?
• Vehicle tank
A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold?
• Red diplomas
The numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase?
• Calories 2
Ben eats approximately 2400 calories per day. His wife Sarah eats 5/8 as much. How many calories does Sarah eat per day?
• Expressions
Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n
• The cube
The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
• Excavation
Excavation for the base of the cottage has dimensions 4.5 m x 3.24 m x 60 cm. The excavated soil will increase its volume by one-quarter. Calculate the volume of excavated soil.