# Fraction calculator

This calculator divides fractions. The first step makes the reciprocal value of the second fraction - exchange numerator and denominator of 2nd fraction. Then multiply both numerators and place the result over the product of both denominators. Then simplify the result to the lowest terms or a mixed number.

## The result:

### 9/22 : 12/11 = 3/8 = 0.375

Spelled result in words is three eighths.### How do we solve fractions step by step?

- Divide: 9/22 : 12/11 = 9/22 · 11/12 = 9 · 11/22 · 12 = 99/264 = 33 · 3 /33 · 8 = 3/8

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 12/11 is 11/12) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 33 gives 3/8.

In other words - nine twenty-seconds divided by twelve elevenths is three eighths.

#### 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

• multiplying a fraction by a whole number: 6 * 3/4

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction

• 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 evaluate from left to right.

## Fractions in word problems:

- Divide 42

Divide. Write your answer in lowest terms as a proper or improper fraction. (8/25)÷(-4/5) - A seller

A seller sliced some pizza into eights. After selling 57 slices, seven slices were left. How many whole pizzas did the vendor slice? - Two boxes 3

Two boxes of pizza of the same size are left on the table. One box has 1/2 of a pizza, and the other has 3/4 of a pizza left in it. Then, Mother divides all the pizzas into 1/8 each. How many were many slices of pizza left? - Convert 6

Convert to a decimal 15/100. - Pieces of wood

How many pieces of wood can each student have if there are 12 pieces and each student needs 1/4 of a piece? - There 20

There is 1/2 of a pizza left for four friends to share. What fraction of a pizza will each friend get to eat? - Divide fractions by half

Find the result of division by half: 3/4 : 1/2 =? - Divide 13

Divide. Simplify your answer and write it as an improper fraction or whole number. 14÷8/3 - Barbara 2

Barbara gets six pizzas to divide equally among four people. How much pizza can each person have? - How many 24

How many are 1/4 cup servings of raisins in 5/8 cup of raisins? - 4 friends

Four friends share 5/6 of a pizza. What fraction of the pizza does each person get? - Two kids

Two kids are sharing 3/5 of a pizza. What fraction of a whole pizza will each kid get? - Pie division

5/8 of a pie divided into six pieces. Each friend got 1/6. What fraction of the whole pie does each person receive? - The bread

There are 12 slices of bread, and each person gets 3/4 of a slice of bread. How many people get bread? - 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?

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