# 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:

### 2 1/2 - 2/3 = 11/6 = 1 5/6 ≅ 1.8333333

The spelled result in words is eleven sixths (or one and five sixths).### How do we solve fractions step by step?

- Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2

b) Add the answer from the previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs. - Subtract: 5/2 - 2/3 = 5 · 3/2 · 3 - 2 · 2/3 · 2 = 15/6 - 4/6 = 15 - 4/6 = 11/6

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(2, 3) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five halfs minus two thirds is eleven sixths.

### 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 chocolate 2

A chocolate cake is cut into twelve equal pieces. Mr. Greedy eats five pieces at break time with his mug of tea. What fraction of the cake is left? - A cake

A cake has 46 slices. Harry ate 16 slices, and Jack ate 26 slices, Dave ate 0 & Mary ate 1 slice. What fraction of the cake is remaining? - You have 2

You have 6/13 of a pie. If you share 9/10, how much will you have left? - Orchard 5421

The orchard has 600 apple trees. On the first day, they cut 1/5 and 2/8 of the total number of trees on the second day. How many more trees do they have to harvest?

- Pizza 16

Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza? - Mario 4

Mario renames the mixed numbers to fractions greater than 1 to find 4 and 1/2 - 2 and 2/3. Which fractions should Mario use to find the difference? Group of answer choices - Second 82446

Petr read ⅜ of the book in the first week, ¼ of the book in the second week, and ⅒ of the book in the third week. The book has 240 pages. How many pages does Peter have left to read?

more math problems »

Last Modified: August 1, 2024