# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 9 1/6 - 5 1/3 = 23/6 = 3 5/6 ≅ 3.8333333

Spelled result in words is twenty-three sixths (or three and five sixths).### How do we solve fractions step by step?

- Conversion a mixed number 9 1/6 to a improper fraction: 9 1/6 = 9 1/6 = 9 · 6 + 1/6 = 54 + 1/6 = 55/6

To find a new numerator:

a) Multiply the whole number 9 by the denominator 6. Whole number 9 equally 9 * 6/6 = 54/6

b) Add the answer from the previous step 54 to the numerator 1. New numerator is 54 + 1 = 55

c) Write a previous answer (new numerator 55) over the denominator 6.

Nine and one sixth is fifty-five sixths. - Conversion a mixed number 5 1/3 to a improper fraction: 5 1/3 = 5 1/3 = 5 · 3 + 1/3 = 15 + 1/3 = 16/3

To find a new numerator:

a) Multiply the whole number 5 by the denominator 3. Whole number 5 equally 5 * 3/3 = 15/3

b) Add the answer from the previous step 15 to the numerator 1. New numerator is 15 + 1 = 16

c) Write a previous answer (new numerator 16) over the denominator 3.

Five and one third is sixteen thirds. - Subtract: 55/6 - 16/3 = 55/6 - 16 · 2/3 · 2 = 55/6 - 32/6 = 55 - 32/6 = 23/6

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, 3) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 3 = 18. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - fifty-five sixths minus sixteen thirds is twenty-three 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) |

## Fractions in word problems:

- Peter's calculation

Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - A man 9

A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - Before 4

Before a journey, the petrol gauge showed my car's tank was half full. When I returned home, it was one-third full. What fraction of a tank of petrol had I used? - Fraction expression

Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - A housewife

A housewife spent 3/7 of her money in the market and 1/2 of the remainder in the shop. What fraction of her money is left?

more math problems »