# 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:

### 1 1/4 - 5/6 = 5/12 ≅ 0.4166667

The spelled result in words is five twelfths.### How do we solve fractions step by step?

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

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

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 4.

One and one quarter is five quarters. - Subtract: 5/4 - 5/6 = 5 · 3/4 · 3 - 5 · 2/6 · 2 = 15/12 - 10/12 = 15 - 10/12 = 5/12

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(4, 6) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 6 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five quarters minus five sixths is five twelfths.

### 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? - Paul ate

Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents? - Difference of two fractions

What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. ) - The recipe

The recipe they are following requires 7/8 cups of milk. Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?

- King

King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers? - Attending school

Huang lives 1/4 of a mile from school, while Lily lives 2/3 of a mile from school. How much further does Lily live from school than Huang? - Free time club

There are 60 children in a club 1/3 of them play football, 2/5 of them play cricket, and the rest play basketball. How many children play basketball

more math problems »

Last Modified: August 1, 2024