# 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:

### -3/5-(-1/4) = -7/20 = -0.35

The spelled result in words is minus seven twentieths.### How do we solve fractions step by step?

- Unary minus: -3/5 = -3/5
- Subtract: the result of step No. 1 - (-1/4) = -3/5 - (-1/4) = -3/5 - -1/4 = -3 · 4/5 · 4 - (-1) · 5/4 · 5 = -12/20 - (-5/20) = -12 - (-5)/20 = -7/20

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(5, 4) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 4 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - minus three fifths minus minus one quarter is minus seven twentieths.

### 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:

- Soup 4

Cornell makes 11/12 of a gallon of soup. He eats equal portions of soup for 5 days, with no soup remaining after the 5th day. How many gallons of soup did Cornell eat each day? - David 4

David made 4/3 of a quart of fruit juice. Each mug he has holds 1/3 of a quart. How many mugs will David be able to fill? - Convert 4

Convert 2 7/10 into an improper fraction. - Learnes

There are 800 learners in a school 7/8 of the learners walk to school. How many learners walk in school?

- Examination 7504

Class 7B is having a preventive dental check-up. Two dental caries were found in a quarter of the pupils and one caries in an eighth. Half of the class had all their teeth healthy. How many pupils go to class 7B if three pupils are absent on the day of th - Pears

There were pears in the basket. I took two-fifths of them and left six in the basket. How many pears did I take? - Sum of the fractions

Find the sum, express your answer to lowest terms. 1. 1/4 + 2/4= 2. 1/6 + 3/6= 3. 6/10 + 2/10= 4. ¾ + ⅛= 5. 5 3/5 + 2 ½=

more math problems »

Last Modified: July 13, 2024