# 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:

### 1/3 / 5 = 1/15 ≅ 0.06666667

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

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

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 5/1 is 1/5) 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 third divided by five is one fifteenth.

#### 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:

- One half 2

One-half pizza will be divided among three pupils. Each pupil receives 1/6. Is it true or false? - Julian 2

Julian and two of his friends will share 1/4 of a pizza. How much will each person get? - A baker 3

A baker made three cakes which were cut into eighths, ready for individual sale. A customer bought three slices or ⅜ of one of the eight cakes. How many slices were left for sale? - The bread

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

Find the quotient of 3/4 and 1/4. - Three 210

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

What is the reciprocal for 4/3? ("RECIPROCAL" is the math word for when we FLIP a fraction...Example: the reciprocal of 3/4 is 4/3.) - 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? - Convert 6

Convert to a decimal 15/100. - Pizza 5

You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get? - Four people

Four people want waffles for breakfast. There are six waffles left. How can six waffles be shared equally among four people? How much does each person get? Draw a picture and write a division expression to model the problem. - 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? - Divide 42

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

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