# Fraction calculator

This calculator divides an integer (or whole number) by a fraction. To divide an integer by a fraction, multiply the denominator by the integer and place it over the numerator. Then simplify the result to the lowest terms or a mixed number.

## The result:

### 8 ÷ 2/3 = 12/1 = 12

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

- Divide: 8 : 2/3 = 8/1 · 3/2 = 8 · 3/1 · 2 = 24/2 = 2 · 12 /2 · 1 = 12

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 2/3 is 3/2) 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 2 gives 12/1.

In other words - eight divided by two thirds is twelve.

#### 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 signs 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• 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 /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

- Fraction and a decimal

Write as a fraction and a decimal. One and two plus three and five hundredths - A class IV.A

In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys? - Lowest terms 2

We can write the expression 4/12 in its lowest term as 1/3. What is 3/15 expressed in its lowest term? - Max has 2

Max has 13 pairs of socks. From this, six pairs are blue, three pairs are brown, two are black, and two are white. What fraction of Max's socks are either brown or black? - A farm 6

A farm has 20 animals. There are four chickens. What fraction of the animals are chickens? Express your answer as a fraction in the simplest form. - In fractions

An ant climbs 2/5 of the pole in the first hour and climbs 1/4 of the pole in the next hour. What part of the pole does the ant climb in two hours? - Evaluate expression

Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2 - Fruit basket

If there are seven apples and five oranges in the basket, what fraction of oranges are in the fruit basket? - Andy gets

Andy gets five out of 15 questions wrong in his math test. What fraction of the question does andy answer correctly? - Mathew

Mathew has eight pencils. Three of them do not have erasers on end. What fraction of the pencils do not have erasers on end? - Fraction to decimal

Write the fraction 3/22 as a decimal.

more math problems »