# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 3.875 31/8 = 3 7/8

Spelled result in words is thirty-one eighths (or three and seven eighths). =### How do we solve fractions step by step?

- Conversion a decimal number to a fraction: 3.875 = 3875/1000 = 31/8

a) Write down the decimal 3.875 divided by 1: 3.875 = 3.875/1

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

3.875/1 = 38.75/10 = 387.5/100 = 3875/1000

Note: 3875/1000 is called a*decimal fraction*.

c) Simplify and reduce the fraction

3875/1000 = 31 * 125/8 * 125 = 31~~* 125~~/8~~* 125~~= 31/8

#### 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:

- 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? - 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. - Denominator 2

The denominator of a fraction is five, and the numerator is 7. Write the fraction. - Fraction and a decimal

Write as a fraction and a decimal. One and two plus three and five hundredths - Someone

Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten? - 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. - 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 - 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? - A company

A company has 860 employees, of which 500 are female. Write a fraction to represent the female employees in the company. - A class IV.A

In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys? - Evaluate expression

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

Reduce the fraction 16/24 to the lowest terms. - Fruit basket

If there are seven apples and five oranges in the basket, what fraction of oranges are in the fruit basket? - Fraction to decimal

Write the fraction 3/22 as a decimal. - The parsley

Milka's grandmother planted 12 rows of vegetables. 1/6 of the rows are carrots. The rest is parsley. How many rows are planted with parsley?

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