# 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:

### (1/6) : (1/2) = 1/3 ≅ 0.3333333

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

- Divide: 1/6 : 1/2 = 1/6 · 2/1 = 1 · 2/6 · 1 = 2/6 = 2 · 1 /2 · 3 = 1/3

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 1/2 is 2/1) 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 1/3.

In other words - one sixth divided by one half is one third.

### 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:

- Soup 4

Cornell makes 11/12 of a gallon of soup. He eats equal portions of soup for 5 days, with no soup remaining after the 5th day. How many gallons of soup did Cornell eat each day? - What 82170

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

Benson spends ⅓ of his pocket money on transport and ⅔ on food I. What fraction of his pocket money did he spend on transport and food? ii. What fraction is left? - A piece 9

A piece of string is 1 4/5 meters long. How many 3/10 meter-long strings can you cut from it?

- Mansour

Mansour has 1/2 kilo of mangoes to divide equally into 8 different bags. What fraction of a kilo will be in each bag? - Tristan

Tristan normally wrestles at 80 pounds. He wants to add enough weight to move into the 84-pound division. What percent of his current body weight must he add? - 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. - Chocolate

Children break chocolate first to third and then every part of another half. What kind got each child? Draw a picture. What part would have been received if each piece had halved? - A string

A string 2 4/5 m long is cut into 6 pieces. How long is each piece?

- Pupils - boys and girls

5/8 of the pupils in a hall were boys. 7/10 of the boys wore glasses. 48 boys didn't wear glasses. How many pupils were there in the hall? - Jacob 4

Jacob is dividing 5 aquariums into 1/8 of aquarium sections for his different animals. How many 1/8s are there in Jacobs 5 aquariums? - The quotient of two numbers

Find the quotient of 229.12 and 12.32 - Division of money

Calculate how many euros Matthew, Miriam, Lucy, Michael, and Janka, when together, have 2,700 euros, and the amounts are at a ratio of 1:5:6:7:8. - 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?

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