# Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 4 7/8 + 2 3/8 = 29/4 = 7 1/4 = 7.25

The spelled result in words is twenty-nine quarters (or seven and one quarter).### How do we solve fractions step by step?

- Conversion a mixed number 4 7/8 to a improper fraction: 4 7/8 = 4 7/8 = 4 · 8 + 7/8 = 32 + 7/8 = 39/8

To find a new numerator:

a) Multiply the whole number 4 by the denominator 8. Whole number 4 equally 4 * 8/8 = 32/8

b) Add the answer from the previous step 32 to the numerator 7. New numerator is 32 + 7 = 39

c) Write a previous answer (new numerator 39) over the denominator 8.

Four and seven eighths is thirty-nine eighths. - Conversion a mixed number 2 3/8 to a improper fraction: 2 3/8 = 2 3/8 = 2 · 8 + 3/8 = 16 + 3/8 = 19/8

To find a new numerator:

a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8

b) Add the answer from the previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 8.

Two and three eighths is nineteen eighths. - Add: 39/8 + 19/8 = 39 + 19/8 = 58/8 = 2 · 29/2 · 4 = 29/4

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(8, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the following intermediate step, cancel by a common factor of 2 gives 29/4.

In other words - thirty-nine eighths plus nineteen eighths is twenty-nine quarters.

### 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: July 23, 2024