# 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 * 2/3 = 2/15 ≅ 0.1333333

Spelled result in words is two fifteenths.### How do you solve fractions step by step?

- Multiple: 1/5 * 2/3 = 1 · 2/5 · 3 = 2/15

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2, 15) = 1. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - one fifth multiplied by two thirds = two 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:

• adding fractions: 2/4 + 3/4• 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:

- Equation with x

Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9 - Andre

Andre, Thomas, and Ivan split 88 postage stamps in a 2:5:4 ratio. How much did Thomas get? - Fraction of a fraction

What is two-quarters of twelve? - Ratio 11

Simplify this ratio 10 : 1/4 - Holiday trip

Pavel is saving for the holiday trip. He received 1100 CZK from his father. He saved a fifth himself and received the rest 500 CZK from his mother. How much did his holiday trip cost? - 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? - Fractions mul add sum

To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get? - 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? - The perimeter 2

The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m? - Prospering students

There are girls and 30 boys in the class. Boys prospering 28, girls all. How many girls are in the class and how many boys are there, if all the prospering students are 95%? - Percent calculation

Calculate 8% if 44% is 32. - Day

What part of the day are 23 hours 22 minutes? Express as a decimal number. - Family party

Anna has 5 €, Anezka has 4,60 € and for all the money they want to buy desserts for a family party. They decide between cakes and pinwheel: The pinwheel is € 0.40 more expensive than the cake, and the cakes can be bought for all the money by a third more

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