# 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:

### 16 3/8 - 9 5/8 = 27/4 = 6 3/4 = 6.75

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

- Conversion a mixed number 16 3/8 to a improper fraction: 16 3/8 = 16 3/8 = 16 · 8 + 3/8 = 128 + 3/8 = 131/8

To find a new numerator:

a) Multiply the whole number 16 by the denominator 8. Whole number 16 equally 16 * 8/8 = 128/8

b) Add the answer from the previous step 128 to the numerator 3. New numerator is 128 + 3 = 131

c) Write a previous answer (new numerator 131) over the denominator 8.

Sixteen and three eighths is one hundred thirty-one eighths. - Conversion a mixed number 9 5/8 to a improper fraction: 9 5/8 = 9 5/8 = 9 · 8 + 5/8 = 72 + 5/8 = 77/8

To find a new numerator:

a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/8 = 72/8

b) Add the answer from the previous step 72 to the numerator 5. New numerator is 72 + 5 = 77

c) Write a previous answer (new numerator 77) over the denominator 8.

Nine and five eighths is seventy-seven eighths. - Subtract: 131/8 - 77/8 = 131 - 77/8 = 54/8 = 2 · 27/2 · 4 = 27/4

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 27/4.

In other words - one hundred thirty-one eighths minus seventy-seven eighths is twenty-seven 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:

- Dividends

The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least? - Buing

Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK? - Dogs weights

Four out of nine dogs weigh less than 20 pounds. What is the decimal equivalent for the number of dogs weighing less than 20 pounds? - Simplest form of a fraction

Which one of the following fractions is not equal to 3/2 after reducing to the simplest form? a) 15/20 b) 12/8 c) 27/18 d) 6/4

- Torque

Torque and Mari each multiplied 1/8 inch times 5/8 inch. Tartaric 5/8 squares point inches. And Marie got 5/64 squared thought inches tall. Which student found a corrupt area? - Ten fractions

Write ten fractions between 1/3 and 2/3 - Steve 3

Steve is making breakfast. The recipes call for 7/8 cup of milk for grits and 3/4 cup for biscuits. He only has 2 cups of milk. Does he have enough to make his breakfast?

more math problems »

Last Modified: June 4, 2024