# 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:

### 8 1/8 - 4 3/8 = 15/4 = 3 3/4 = 3.75

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

- Conversion a mixed number 8 1/8 to a improper fraction: 8 1/8 = 8 1/8 = 8 · 8 + 1/8 = 64 + 1/8 = 65/8

To find a new numerator:

a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8

b) Add the answer from the previous step 64 to the numerator 1. New numerator is 64 + 1 = 65

c) Write a previous answer (new numerator 65) over the denominator 8.

Eight and one eighth is sixty-five eighths. - Conversion a mixed number 4 3/8 to a improper fraction: 4 3/8 = 4 3/8 = 4 · 8 + 3/8 = 32 + 3/8 = 35/8

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 3. New numerator is 32 + 3 = 35

c) Write a previous answer (new numerator 35) over the denominator 8.

Four and three eighths is thirty-five eighths. - Subtract: 65/8 - 35/8 = 65 - 35/8 = 30/8 = 2 · 15/2 · 4 = 15/4

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 15/4.

In other words - sixty-five eighths minus thirty-five eighths is fifteen 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:

- Collected 58291

Veronika collected 3/5 kg of paper, Alex collected 3/4 kg of paper, and Juraj collected 7/10 kilograms of paper. a) who collected the most and who collected the least? b) how many kg of paper did they collect together? (cut the result in the form of a mix - Stephan - cookies

Stephan is making cookies for the class. He has a recipe that calls for 3 and 1/2 cups of flour. He has 7/8 a cup of wheat flour and 2 and 1/2 cups white flour. Does Mr. Stephan have enough flour to make the cookies? - Ordered pairs

Given: Set T = {(1,2), (2,3), (3,4), (4,5), (5,5), (6,7), (6,6), (7,8), (8,9), (9,9), (9, 10), (11,12), (12,13), (13,14), (15,16), (16,16), (17,18), (18,19), (20,21)} Find the probability of having an ordered pair wherein the second element is greater tha - Indicated 32771

Did Sonia not like the ratio indicated on the jelly sugar; which picture is wrong and why? A) for 1000g of fruit, add 350g of sugar 3:1: super jelly sugar B) 3:1 for 1500 g of fruit, add 500 g of sugar: extra jelly sugar

- Measuring 36483

Dominik teaches his kitten to go to the cat toilet for litter. He needs to fill the toilet halfway, but he needs to know how many bales of litter to buy. Please advise him if you know that the toilet has a bottom measuring 0.43 m and 3.5 dm and is 11 cm d - The fuel

The car's fuel was ¾ full at the beginning of the week. At the end of the week, there was ⅛ of a tank left. a. Did the car use more or less than ½ of a fuel tank? How do you know? b. How much more or less than ½ of a tank did it use? Show your work using - Drill bit

Bill's 3/8 inch drill bit is missing and is needed for a job. He can get by with drilling a smaller hole than 3/8 inch as long as it is as close to 3/8 inch as possible. Which of the following bits would be the best to use? A. 13/32 inch B. 23/64 inch C.

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Last Modified: July 22, 2024