# 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:

### 5/6 + 8/9 - 7/12 = 41/36 = 1 5/36 ≅ 1.1388889

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

- Add: 5/6 + 8/9 = 5 · 3/6 · 3 + 8 · 2/9 · 2 = 15/18 + 16/18 = 15 + 16/18 = 31/18

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

In other words - five sixths plus eight ninths is thirty-one eighteenths. - Subtract: the result of step No. 1 - 7/12 = 31/18 - 7/12 = 31 · 2/18 · 2 - 7 · 3/12 · 3 = 62/36 - 21/36 = 62 - 21/36 = 41/36

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(18, 12) = 36. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 18 × 12 = 216. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirty-one eighteenths minus seven twelfths is forty-one thirty-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

• 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:

- Using money

Out of 575,000.00 given to a school, an amount of 25,000.00 was used. What fraction of the total amount was used? - Someone

Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten? - A less than B

What is 3/5 less than 11/12? (Answer should be in proper or improper only: Example 1/2, -1/2, 3/2, and -3/2) - Fraction 77774

Express the value of the fraction 25/12 as a decimal number.

- Pupils 13

If ⅜ of the pupils in year 9 say, their favorite color is red. There are 112 pupils in year 9. How many students said red is their favorite color? - A baker 3

A baker made three cakes which were cut into eighths, ready for individual sale. A customer bought three slices or ⅜ of one of the eight cakes. How many slices were left for sale? - Probability RGB

The bag has six red, five green, eight blue, and 11 yellow balls. What is the probability that we will pull out a green ball?

more math problems »

Last Modified: September 8, 2024