# 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:

### 2/3 ÷ 4/5 = 5/6 ≅ 0.8333333

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

- Divide: 2/3 : 4/5 = 2/3 · 5/4 = 2 · 5/3 · 4 = 10/12 = 2 · 5 /2 · 6 = 5/6

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 4/5 is 5/4) 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 5/6.

In other words - two thirds divided by four fifths is five sixths.

#### 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:

- The following 3

The following fraction is reduced to its lowest terms except one. Which of these: A.98/99 B.73/179 C.1/250 D.81/729 - Simplify 12

Simplify {1/3 + 1/12} ÷ {2/3 - 5/8} - Children 9

There are 11 children in a room. Six of the children are girls. What fraction of the children are girls? - 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? - Denominator 2

The denominator of a fraction is five, and the numerator is 7. Write the fraction. - In the cafeteria

There are 18 students in Jacob's homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria? - Value of Z

For x = -9, what is the value of Z, where Z equals fraction numerator x minus 17 over denominator 6.5 end fraction. Give your answer to 2 decimal places. - Reduce 9

Reduce the fraction 16/24 to the lowest terms. - Zdeněk

Zdeněk picked up 15 l of water from a 100-liter full-water barrel. Write a fraction of what part of Zdeněk's water he picked. - Evaluate expression

Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2 - Brown or black

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? - Fraction to decimal

Write the fraction 3/22 as a decimal. - A quarter

A quarter of the number 72 is: - Fruit basket

If there are seven apples and five oranges in the basket, what fraction of oranges are in the fruit basket? - Fractions 80134

There are 420 pupils in the school. Two hundred fifty-two pupils go to the 1st level. Write as a fraction what part of the pupils goes to the 1st grade and what part to the 2nd grade. Shorten both fractions to their basic form.

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