# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 5 : (1/4) = 20/1 = 20

The spelled result in words is twenty.### How do we solve fractions step by step?

- Divide: 5 : 1/4 = 5/1 · 4/1 = 5 · 4/1 · 1 = 20/1 = 20

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 1/4 is 4/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

In other words - five divided by one quarter is twenty.

### 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:

- What 82170

What part of €24 is €12, €4, €8, €1, €18, €20? - 7 athletes

Seven athletes run a combined total of 4 miles. How many miles did each athlete run? - A ribbon

Bree has a piece of ribbon that is 6 inches long. She needs to cut it into equal pieces measuring 3/4 of an inch. How many pieces will she have? Answer in simplest form - My fraction

My fraction is not a mixed number. My fraction is equivalent to 1/2. When my fraction is divided by 1/3, the answer is 1 1/2. The numerator of the fraction is 4. What is my fraction?

- Ciara’s

Ciara's father bought a big bar of chocolate at the grocery. He divided it into two equal pieces and gave one piece to Ciara. Ciara then shared her piece with her and her two friends. What fraction of the big bar of chocolate did one of Ciara's friends ge - Tristan

Tristan normally wrestles at 80 pounds. He wants to add enough weight to move into the 84-pound division. What percent of his current body weight must he add? - Lila knows

Lila knows that 3/16 means "3 divided by 16." She uses this to find the decimal equivalent for 3/16. Enter a digit into each box to continue her work. - Unit rate

Find unit rate: 6,840 customers in 45 days - Health department

A survey by the state health department found that the average person ate 208 pounds of vegetables last year and 5 125 8 pounds of fruit. What fraction of the total pounds of fruit and vegetables do the pounds of fruits represent?

- Pupils - boys and girls

5/8 of the pupils in a hall were boys. 7/10 of the boys wore glasses. 48 boys didn't wear glasses. How many pupils were there in the hall? - 2/3 write

2/3 write it in an equivalent decimal - Jacob 4

Jacob is dividing 5 aquariums into 1/8 of aquarium sections for his different animals. How many 1/8s are there in Jacobs 5 aquariums? - Container

How many three-quarters liters jars fill 30 liters containers? - Soup from canteen

For how many people is 90 liters of soup enough if we assume 3/8 liters of soup per person in the canteen?

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