# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### (2/3) : (4/5) = 5/6 ≅ 0.8333333

The spelled result in words is five sixths.### How do we solve fractions step by step?

- Divide: 2/3 : 4/5 = 2/3 · 5/4 = 2 · 5/3 · 4 = 10/12 = 2 · 5 /2 · 6 = 5/6

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 4/5 is 5/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 5/6.

In other words - two thirds divided by four fifths is five sixths.

### Rules for expressions with fractions:

**Fractions**- use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter

**5/100**. If you use mixed numbers, leave a space between the whole and fraction parts.

**Mixed numerals**(mixed numbers or fractions) keep one space between the integer and

fraction and use a forward slash to input fractions i.e.,

**1 2/3**. An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e.,

**1/2 : 1/3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

### Math Symbols

Symbol | Symbol name | Symbol Meaning | Example |
---|---|---|---|

+ | plus sign | addition | 1/2 + 1/3 |

- | minus sign | subtraction | 1 1/2 - 2/3 |

* | asterisk | multiplication | 2/3 * 3/4 |

× | times sign | multiplication | 2/3 × 5/6 |

: | division sign | division | 1/2 : 3 |

/ | division slash | division | 1/3 / 5 |

: | colon | complex fraction | 1/2 : 1/3 |

^ | caret | exponentiation / power | 1/4^3 |

() | parentheses | calculate expression inside first | -3/5 - (-1/4) |

#### 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

• reciprocal of a fraction: 1 : 3/4

• square of a fraction: 2/3^2

• cube of a fraction: 2/3^3

• exponentiation of a fraction: 1/2^4

• 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) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction

• 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

**the 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.

**MDAS**- Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.

Be careful; always do

**multiplication and division**before

**addition and subtraction**. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.

## Fractions in word problems:

- What 82170

What part of €24 is €12, €4, €8, €1, €18, €20? - Division of mixed

What is 1 3/8 ÷ 6 7/10? Reduce your answer to the lowest terms. - Lila knows

Lila knows that 3/16 means "3 divided by 16." She uses this to find the decimal equivalent for 3/16. Enter a digit into each box to continue her work. - Which 11

Which decimal is equivalent to 5/6

- Five-eighth 61644

The glass can hold five-eighth liters of water. How many glasses would we fill with two five-liter bottles? - Fraction of a fraction

What is two-quarters of twelve? - Multiply 63734

What result do we get if we multiply 1/5 of 600 by three and divide the result by 1/10 of 100? - Hectoliters 63294

The lemonade is filled into 1/3 liter bottles. How many bottles must be used to fill two hectoliters of lemonade? - The jeep

The jeep driver filled his tank with 12 3/4 liters of gasoline. If he uses 1 1/3 liters for each round trip, how many round trips can he make before re-filling?

- Two teacher 2

Two teachers are paid 5100 USD together. If the teachers are to share this amount in the ratio of 3:7, how much does each receive? - Knitting a scarf

Rebecca is knitting a scarf. She runs out of yarn when the scarf is 1 1/2 feet long, which is ⅔ of the length she wants to make. How long is the scarf when finished? Write a multiplication and division equation to represent this situation. - Consumes 7282

A person consumes 20 grams of oxygen in 1 hour, and a jet aircraft up to 3 total of 3/4 tons. How much more oxygen does an airplane use per hour than a human? - Percent calculation

Calculate 8% if 44% is 32. - Money spending

Albert and Peter have an amount of money. If Albert spent $6 and Peter did not spend any, then the ratio of Albert's money to Peter's money is 1:3 . If Peter spent $6 and Albert did not spend any, the ratio of Albert's money to Peter's money is 3:7.How mu

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