# 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:

### 1/5 + 1/5 + 1/5 = 3/5 = 0.6

Spelled result in words is three fifths.

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

1. Add: 1/5 + 1/5 = 1 + 1/5 = 2/5
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(5, 5) = 5. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 5 = 25. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one fifth plus one fifth = two fifths.
2. Add: the result of step No. 1 + 1/5 = 2/5 + 1/5 = 2 + 1/5 = 3/5
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(5, 5) = 5. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 5 = 25. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - two fifths plus one fifth = three fifths.

#### 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:

• One third
If 3/5 is 360, how much is 1/3?
• Equation 20
In given equation: 8/9-4/5=2/9+x, find x
• UN 1
If we add to an unknown number his quarter, we get 210. Identify unknown number.
• Dividends
The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
• Unit rate
Find unit rate: 6,840 customers in 45 days
• Tallest and shortest
Jenn is the tallest on the team. He is 1 1/2 times as tall as the shortest girl whom is 4 1/4 feet tall. How tall is Jebb?
• Roses and tulips
At the florist are 50 tulips and 5 times fewer roses. How many flowers are in the flower shop?
• Value 4
If 5/18=425, what is the value 13/18?
• Tractors
6 tractors started plowing the field that they together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
• Buing
Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK?
• Dice and coin
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
• Reducing scale
I am sizing some landscaping and I measured everything for a 20 to 1 scale. I realized when I was done that it was at 30 to 1. How can I convert what I already have to 30 to 1. (Example, grass area is 22,871.6' at 20 to 1, how do you figure it out to be 3
• Pamela
Lara Pamela spends her salary of 3000 for food, clothing, recreation and savings, which are in the ratio of 48:20:15:37, respectively. How much does he spend for savings?