# 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:

### 8 4/6 - 5 8/12 = 3/1 = 3

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

- Conversion a mixed number 8 4/6 to a improper fraction: 8 4/6 = 8 4/6 = 8 · 6 + 4/6 = 48 + 4/6 = 52/6

To find a new numerator:

a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6

b) Add the answer from the previous step 48 to the numerator 4. New numerator is 48 + 4 = 52

c) Write a previous answer (new numerator 52) over the denominator 6.

Eight and four sixths is fifty-two sixths. - Conversion a mixed number 5 8/12 to a improper fraction: 5 8/12 = 5 8/12 = 5 · 12 + 8/12 = 60 + 8/12 = 68/12

To find a new numerator:

a) Multiply the whole number 5 by the denominator 12. Whole number 5 equally 5 * 12/12 = 60/12

b) Add the answer from the previous step 60 to the numerator 8. New numerator is 60 + 8 = 68

c) Write a previous answer (new numerator 68) over the denominator 12.

Five and eight twelfths is sixty-eight twelfths. - Subtract: 52/6 - 68/12 = 52 · 2/6 · 2 - 68/12 = 104/12 - 68/12 = 104 - 68/12 = 36/12 = 12 · 3/12 · 1 = 3

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(6, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 12 = 72. In the following intermediate step, cancel by a common factor of 12 gives 3/1.

In other words - fifty-two sixths minus sixty-eight twelfths is three.

### 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:

- 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? - Miguel 2

Miguel had 5/6 of a pizza, and Chris had 1 and 5/8 of a similar pizza. How much more pizza did Chris have than Miguel? - Mother 16

Mother cooks food in 1 3/4 hours and prepares the children's snack in 4/6 of an hour. How much longer does she cook the food than prepare the children's snacks? - Rice cooking

Aunt had 1 3/4 kg of rice, then Aunt bought another 2 1/2 kg of rice, cooked 0.2 kg, calculate the remaining rice Aunt now.

- Two pieces 2

Two pieces of length 12/5 m and 23/9 m are cut from a rope of length 13 m. Find the length of the remaining rope. - Xero had

Xero had a piece of ribbon. He used 0.4 of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed for a large box is 3 times the length of ribbon needed for a small box. Xero used 5/6 of the remaining ribbon to decorate the presents. a) Wh - 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?

more math problems »

Last Modified: June 4, 2024