# 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:

### 7 2/9 - 3 5/6 = 61/18 = 3 7/18 ≅ 3.3888889

The spelled result in words is sixty-one eighteenths (or three and seven eighteenths).### How do we solve fractions step by step?

- Conversion a mixed number 7 2/9 to a improper fraction: 7 2/9 = 7 2/9 = 7 · 9 + 2/9 = 63 + 2/9 = 65/9

To find a new numerator:

a) Multiply the whole number 7 by the denominator 9. Whole number 7 equally 7 * 9/9 = 63/9

b) Add the answer from the previous step 63 to the numerator 2. New numerator is 63 + 2 = 65

c) Write a previous answer (new numerator 65) over the denominator 9.

Seven and two ninths is sixty-five ninths. - Conversion a mixed number 3 5/6 to a improper fraction: 3 5/6 = 3 5/6 = 3 · 6 + 5/6 = 18 + 5/6 = 23/6

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 5. New numerator is 18 + 5 = 23

c) Write a previous answer (new numerator 23) over the denominator 6.

Three and five sixths is twenty-three sixths. - Subtract: 65/9 - 23/6 = 65 · 2/9 · 2 - 23 · 3/6 · 3 = 130/18 - 69/18 = 130 - 69/18 = 61/18

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(9, 6) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 6 = 54. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - sixty-five ninths minus twenty-three sixths is sixty-one eighteenths.

### 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:

- Slab of a chocolate

Albany has 3/4 of a slab of chocolate he gives 2/5 of the slab to her friend Peter. How much chocolate does she have left? - Pizza 16

Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza? - Mr Peter

Mr Peter bought a pizza. He ate 2/5. His son ate 1/5, and the rest his wife ate. What amount of pizza did his wife eat? - Difference of two fractions

What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. )

- The sum 49

The sum of two rational numbers is -5. If one of them is -13/6, find the other. - A craft

A craft store has a 9-yard spool of ribbon. In the morning, a customer buys 1/5 yd of ribbon. Another customer buys 7/10 yd of ribbon in the afternoon from the spool. How much ribbon is left? - Michael

Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?

more math problems »

Last Modified: October 9, 2024