# 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:

### (4 2/3) : (1/2) = 28/3 = 9 1/3 ≅ 9.3333333

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

- Conversion a mixed number 4 2/3 to a improper fraction: 4 2/3 = 4 2/3 = 4 · 3 + 2/3 = 12 + 2/3 = 14/3

To find a new numerator:

a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3

b) Add the answer from the previous step 12 to the numerator 2. New numerator is 12 + 2 = 14

c) Write a previous answer (new numerator 14) over the denominator 3.

Four and two thirds is fourteen thirds. - Divide: 14/3 : 1/2 = 14/3 · 2/1 = 14 · 2/3 · 1 = 28/3

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/2 is 2/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - fourteen thirds divided by one half is twenty-eight thirds.

### 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:

- Benson

Benson spends ⅓ of his pocket money on transport and ⅔ on food I. What fraction of his pocket money did he spend on transport and food? ii. What fraction is left? - A piece 9

A piece of string is 1 4/5 meters long. How many 3/10 meter-long strings can you cut from it? - A cupcake

A cupcake takes just 1/4 of an hour to bake. How can cupcakes bake in 1 1/2 hours? - Once simplified

Once simplified, which of the expressions below have a value between 20 and 30? Select all that apply. A) 32÷8×514 B) -18÷6×9 C) 4×12÷2 D) 12×413÷(-2)

- Individual 64124

The line is divided into two parts in a ratio of 4:7. The difference in lengths of individual parts is 18 cm. What is the length of the line in cm? - The third

The one-third rod is blue, one-half of the rod is red, and the rest of the rod is white and measures 8 cm. How long is the whole rod? - Product, sum and quotient

If the product of 1 1/6 and 3 2/3 is added to the quotient of 5/7 and 6/7, what is the sum? Write the solution as a mixed number or a fraction in the lowest terms.

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Last Modified: October 9, 2024