# 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:

### 2/3 * 4/5 = 8/15 ≅ 0.5333333

Spelled result in words is eight fifteenths.

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

1. Multiple: 2/3 * 4/5 = 2 · 4/3 · 5 = 8/15
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(8, 15) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - two thirds multiplied by four fifths = eight fifteenths.

#### 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:

• 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?
• 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?
• Sewing
Beth's mother can sew 235 pairs of short pants in 6 days while Lourdes can sew 187 pairs in 8 days. How many more pairs of short pants can Beth's mother sew?
• Master and apprentice
Master painted the roof in 3 hours and apprentice for 4 hours. How many of roof they painted in hour and how many in three quarters of an hour?
• Pumps
6 pump fills the tank for 3 and a half days. How long will fill the tank 7 equally powerful pumps?
• The kennel
20 dogs. Ratio dogs to cats is 3:2  how many cats?
• Alcohol risk
The 2009 Youth Risk Behavior Survey found that about 5 out of 12 high school students drank some alcohol in the 30 days preceding the survey. If a high school has 2400 students, how many would be expected to have used alcohol within a 30-day period?
• Ricky
Ricky painted 3/5 of the side of the garage. When he repainted ½ of this part, what part of the side of the garage did he painted twice?
• Coal mine
The monthly plan of 17,000 tons of coal exceeded the mine by 1/25. How many tonnes of coal have been harvested from the mine above plan?
• 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.
• Lin has
Lin has a cake pan that has a length of 8/3 inches, a width of 15/4 inches and a height of 3/2 inches. What is the volume of the cake pan?
• 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?
• Max vs Sharon
Max is 1 1/2 times as tall as Sharon. Alan is 4 1/3 feet tall. If Alan is 6 inches taller than Sharon, how tall is Max?