# 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:

### 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:

- A man 4

A man has 560 cows. He sells 1/4 of them. How many cows are left? - Decrease 64204

Decrease the number 104 by 3/8 of the given number. - A wheat 2

A wheat bag contains 50kg of wheat. After consuming 2/7 of it, how much wheat is left in a bag? - Mary spends

Mary spends 2 1/8 hours running and also spends 1 5/7 hours at the mall. How much less time does Mary spend at the mall compared to running?

- Jerrie

Jerrie can repair her car in 1 1/12 hours. A mechanic can do the same job in 8/12 hours. How much longer does it take Jerrie to do the job? - Cooking classes

Ms. Wright's two cooking classes are making a total of 60 sweet potato pies. Each pie requires 2 1/4 sweet potatoes. Her first class makes 1/3 of the total number of pies needed. Exactly how many sweet potatoes will her second class need in order to make - Peter 10

Peter covered 1/2 of the journey on Monday, 1/4 of the remainder on Tuesday, and the rest on Wednesday. What fraction of the journey was covered on the two days?

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Last Modified: October 9, 2024