# 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:

### 3 4/6 + 9/18 = 25/6 = 4 1/6 ≅ 4.1666667

The spelled result in words is twenty-five sixths (or four and one sixth).### How do we solve fractions step by step?

- Conversion a mixed number 3 4/6 to a improper fraction: 3 4/6 = 3 4/6 = 3 · 6 + 4/6 = 18 + 4/6 = 22/6

To find a new numerator:

a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6

b) Add the answer from the previous step 18 to the numerator 4. New numerator is 18 + 4 = 22

c) Write a previous answer (new numerator 22) over the denominator 6.

Three and four sixths is twenty-two sixths. - Add: 22/6 + 9/18 = 22 · 3/6 · 3 + 9/18 = 66/18 + 9/18 = 66 + 9/18 = 75/18 = 3 · 25/3 · 6 = 25/6

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 18) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 18 = 108. In the following intermediate step, cancel by a common factor of 3 gives 25/6.

In other words - twenty-two sixths plus nine eighteenths is twenty-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:

- Evaluate 40

Evaluate a+bc-d if a=78, b=-716, c=0.8, and d=14 . Write your answer as a fraction in simplest form. - 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? - The bucket

Anna and Joey share an 18-ounce bucket of clay. By the end of the week, Anna has used 1/3 of the bucket, and Joey has used 2/3 of the bucket of clay. How many ounces are left in the bucket? - Matthew

Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far?

- Joe had

Joe had a full tank of petrol in his car. His car consumed 2/9 of the tank of petrol on Saturday and 1/3 of it on Sunday. What fraction of the tank of petrol was left after the weekend? - Ahsan

Ahsan has a large pizza. He gives 1/3 to his sister and 1/4 to his mother. What fraction of the pizza does Ahsan have left? - Rica has

Rica has 3 pieces of lace, each measuring 1/7 meter, 5/14 meter, and 3/7 meter. How long are the pieces of lace together? - Transparent 5345

Clay balls and several transparent glass balls spilled out of Peter's pouch. Color the balls one by one if you know that 1/6 were red, 3/8 were blue, 7/24 were green, and 1/12 were yellow. How many glasses did he have? - Summands 5215

Divide the number into two summands, which are in the given ratio: a) 3, 11:4 b) 5.1 8:9 c) 1 7:3 d) 0.42 1:6

- Roses and tulips

At the florist are 50 tulips and five times fewer roses. How many flowers are in the flower shop? - Conversion of units

Complete the following length of data - Ayden

Ayden is 140 cm tall, and his friend Alex is 1/5 taller than him. How tall is Alex? - The numerator

The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction? - Arithmetic 81795

In which arithmetic sequence is S5=S6=60?

more math problems »