# Fraction calculator

This calculator divides a fraction by an integer or a whole number. To divide a fraction by a whole number, we divide the denominator by the whole number. Then simplify the result to the lowest terms or a mixed number.

## The result:

### 1/2 : 3 = 1/6 ≅ 0.1666667

Spelled result in words is one sixth.### How do we solve fractions step by step?

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

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 3/1 is 1/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half divided by three is one sixth.

#### 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:

- Fraction expression

Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - Divide with remainder

Mrs. Diaz has 4 brownies left. She wants to share the brownies equally among her 5 children. Which of the following shows the amount of brownies each child can receive? - 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? - Divide fractions by half

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

Paola has 3/4 of a candy bar. He wants to give 1/8 of the candy bar to each of his friends. How many friends can have 1/8 of the candy bar? - Solve 21

Solve the following problem and write the answer as a mixed number in the lowest terms: 8/11 ÷ 4/9. - Julian 3

Julian had 7 cookie and gave half of them to a friend. How many cookies did his friend get? - Divide 42

Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5) - One half 2

One-half pizza will be divided among three pupils. Each pupil receives 1/6. Is it true or false? - Three 210

Three friends share 4/5 of a pizza. What fraction of pizza does each person get? - Divide 13

Divide. Simplify your answer and write it as an improper fraction or whole number. 14÷8/3 - 4 friends

Four friends share 5/6 of a pizza. What fraction of the pizza does each person get? - 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? - 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? - Divide mixed numbers

Divide the following fractions and reduce your answers to its simplest form if possible: 1. 2 3/4 ÷ 3 1/12 2. 3 2/3 ÷ 4 1/2 3. 5 3/7 ÷ 2 3/9 4. 6 2/3 ÷ 1 1/5

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