# 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:

### 6 4/7 + 5/6 = 311/42 = 7 17/42 = 7.4047619

The spelled result in words is three hundred eleven forty-seconds (or seven and seventeen forty-seconds).### How do we solve fractions step by step?

- Conversion a mixed number 6 4/7 to a improper fraction: 6 4/7 = 6 4/7 = 6 · 7 + 4/7 = 42 + 4/7 = 46/7

To find a new numerator:

a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7

b) Add the answer from the previous step 42 to the numerator 4. New numerator is 42 + 4 = 46

c) Write a previous answer (new numerator 46) over the denominator 7.

Six and four sevenths is forty-six sevenths. - Add: 46/7 + 5/6 = 46 · 6/7 · 6 + 5 · 7/6 · 7 = 276/42 + 35/42 = 276 + 35/42 = 311/42

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(7, 6) = 42. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 6 = 42. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - forty-six sevenths plus five sixths is three hundred eleven forty-seconds.

### 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:

- Work out 2

Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - My whole

My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - Evaluate 27

Evaluate the expression shown below and write your answer as a fraction in the simplest form. (8)/(3)+ (11)/(12) - Adding denominators

Max is working out 2/3+7/9. He says the answer is 9/12. What mistake has Max made?

- Integer add to fraction

Seven is added to the sum of 4/5 and 6/7 - Sum of the fractions

Find the sum, express your answer to lowest terms. 1. 1/4 + 2/4= 2. 1/6 + 3/6= 3. 6/10 + 2/10= 4. ¾ + ⅛= 5. 5 3/5 + 2 ½= - A farmer 8

A farmer uses 1/3 of his land to plant cassava, 1/3 of the remaining land to plant maize, and the rest for vegetables. What fraction did the farmer use to plant vegetables?

more math problems »

Last Modified: September 8, 2024