# Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### (5/6) : (2/3) = 5/4 = 1 1/4 = 1.25

The spelled result in words is five quarters (or one and one quarter).### How do we solve fractions step by step?

- Divide: 5/6 : 2/3 = 5/6 · 3/2 = 5 · 3/6 · 2 = 15/12 = 3 · 5 /3 · 4 = 5/4

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 3 gives 5/4.

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

### 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:

- Chocolate bar sharing

If John has 3/5 of a chocolate bar and wants to share it equally among himself and two friends, how much of the chocolate bar will each person get? - An apple

An apple cake recipe calls for 2 2/3 c of apple slices. Each apple supplies about 2/3 c of slices. How many apples are needed to make the cake? - How many 29

How many 5/8s's are in 1? (To write a whole number and fraction: 2 3/4) - Track suits

There are 100 tracksuits in a box. The sports shop sold 3/10 of the tracksuits on Monday, 1/4 on Tuesday, and they sold 2/5 on Wednesday, and the rest on Thursday. 1. How many tracksuits did the shop sell on Thursday? 2. What fraction of the tracksuits di

- Joel divided

Joel divided a number and got a solution of 8 quarters(1/4). What is the whole number that can be divided into eight quarters? - Division by zero

Fraction 5 by 2. if three is added to the numerator and two is subtracted from the denominator, then the new fraction is: - Third of an hour

How many minutes is a third of an hour? Do you know to find a third of the lesson hour (45min)? - Resulting 6194

Three Americans went to the casino. They put 10,000 CZK into the game. The resulting sum on the game report was CZK 160,000 less. They decided to divide the amount owed equally. Do the math and find out how much everyone owes. - Mr. Ali

Mr. Ali gave 26 liters of orange juice to his 3 kids equally. How much did each kid get?

- Half of the product

What is half the product of 8 1/7 and 7 4/5? - The average 6

The average temperature dropped 16°C over a period of 5 weeks. What is the average change in temperature per week? - Grandma 74594

Grandma planted 150 trees, 1/6 of which were oaks. How many oaks were there? - Max has

Max has a 1/3 of a pound of pretzels and wants to share equal parts between himself and a friend. How many pretzels will Max's friend receive? - Kate shares

Kate shares a 64-ounce bottle of apple cider with five friends. Each person's serving will be the same number of ounces. Between what two whole ounces will each person's serving to be? Explain using division.

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