# 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 5/12 + 3 8/12 = 73/12 = 6 1/12 ≅ 6.0833333

The spelled result in words is seventy-three twelfths (or six and one twelfth).### How do we solve fractions step by step?

- Conversion a mixed number 2 5/12 to a improper fraction: 2 5/12 = 2 5/12 = 2 · 12 + 5/12 = 24 + 5/12 = 29/12

To find a new numerator:

a) Multiply the whole number 2 by the denominator 12. Whole number 2 equally 2 * 12/12 = 24/12

b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29

c) Write a previous answer (new numerator 29) over the denominator 12.

Two and five twelfths is twenty-nine twelfths. - Conversion a mixed number 3 8/12 to a improper fraction: 3 8/12 = 3 8/12 = 3 · 12 + 8/12 = 36 + 8/12 = 44/12

To find a new numerator:

a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/12 = 36/12

b) Add the answer from the previous step 36 to the numerator 8. New numerator is 36 + 8 = 44

c) Write a previous answer (new numerator 44) over the denominator 12.

Three and eight twelfths is forty-four twelfths. - Add: 29/12 + 44/12 = 29 + 44/12 = 73/12

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(12, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 12 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - twenty-nine twelfths plus forty-four twelfths is seventy-three twelfths.

### 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:

- A cake 2

Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen eat? - Numbers 5256

What is 4/5 of the sum of numbers (-4.95) and (-11.05)? - Equal slices of pizza

If you have a pizza divided into 6 equal slices and you eat 2/6 of it, what fraction of the pizza is left? - Negative mixed 2

What is −4 2/3 + 2 1/2? Write the answer as a mixed number in simplest form.

- Negative fractions

I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I? - 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? - Find two 4

Find two fractions between 1/4 and 2/3. How do you know you are right? - Rachel 2

Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether? - Three cakes

There are three cakes an ice cream cake, chocolate, and a sponge cake. We ate 3/4 of the ice cream cake. We cut the chocolate cake into twelve equal pieces, of which We ate nine. The sponge cake was divided into eight equal pieces, with only one remaining

- The sum 42

The sum of two fractions is 6 5/6. If the bigger fraction is subtracted by 3/4, the difference is 4 7/12. What is the smaller fraction? - A miner

A miner is working at an elevation of -64 7/9 and then ascends 22 1/3. What is the miner's new location? - Dexter

Dexter spent 1 2/3 hours working on his history homework and another 2 1/5 hours working on his math homework. How many hours did Dexter spend working on the two homework? - Evaluate 33

Evaluate x+y when x=- 4/5 and y= 1/3. Write your answer as a fraction or mixed number in simplest form. - Jana is

Jana is knitting a blanket; so far, she has 3 1/4 meters finished. She has another 2 2/3 meters left to knit. How long will the blanket be when finished

more math problems »