# 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:

### 1/3 / 5/6 = 2/5 = 0.4

Spelled result in words is two fifths.### How do we solve fractions step by step?

- Divide: 1/3 : 5/6 = 1/3 · 6/5 = 1 · 6/3 · 5 = 6/15 = 3 · 2 /3 · 5 = 2/5

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 5/6 is 6/5) 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 3 gives 2/5.

In other words - one third divided by five sixths is two fifths.

#### 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 be evaluated from left to right.

## Fractions in word problems:

- A quotient

What is the quotient of 3/10 divided by 2/4 as a fraction? - Divide 42

Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5) - Quotient and division

Find the quotient of 3/4 and 1/4. - Division by reciprocal

What is the corresponding illustration/model of 7÷ 1/3? - One fourth

One-fourth of an apple pie is left for two family members to share equally. What fraction of the original pie will each member get? - 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? - Larry 2

Larry spends half of his workday teaching piano lessons. He sees six students and gives the same amount of time to each. What fraction of his workday is spent with each student? - In dividing

In dividing fractions, get the reciprocal of the divisor and change the division symbol to the multiplication symbol. 2/3 : 5/6 - 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? - Fractions 4

How many 2/3s are in 6? - Candy bars

Sheldon has four candy bars and wants to split them among his five friends. If each person gets the same amount, what part of the candy bar will each friend get? Show your work. - Eiko brought

Eiko brought 4/5 of a cake to school. She divided it equally and shared all of it with her 3 friends. How much cake did each friend receive? - What is 16

What is the quotient of 11 over 12 divided by one-third?

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