# Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### (2 1/2) : 7 = 5/14 ≅ 0.3571429

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

- Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2

b) Add the answer from the previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs. - Divide: 5/2 : 7 = 0.35714285714286 = 5/14

### 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

• square root of a fraction: sqrt(1/16)

• 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:

- 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. - 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 - Comparing by height

Ira is 1 2/5 m tall. Her mother is 4/5 m as tall as Ira. How many times is Ira's mother taller than her?

- Twelve

Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each student in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by expression. - Drinking water

A man drinks a keg of water in 36 days, and a woman drinks in 65 days. How many days do they consume a keg together? - Youth track

Youth track from Hronská Dúbrava to Banská Štiavnica, which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate the size of subsidies to a trip group

more math problems »

Last Modified: October 9, 2024