# 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:

### 1/3 / 2/5 = 5/6 ≅ 0.8333333

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

- Divide: 1/3 : 2/5 = 1/3 · 5/2 = 1 · 5/3 · 2 = 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 2/5 is 5/2) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one third divided by two 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:

- David 4

David made 4/3 of a quart of fruit juice. Each mug he has holds 1/3 of a quart. How many mugs will David be able to fill? - A reciprocal

What is the reciprocal for 4/3? ("RECIPROCAL" is the math word for when we FLIP a fraction...Example: the reciprocal of 3/4 is 4/3.) - Soup 4

Cornell makes 11/12 of a gallon of soup. He eats equal portions of soup for 5 days, with no soup remaining after the 5th day. How many gallons of soup did Cornell eat each day? - A lawn

Sean and his sister, Betty, equally mowed 8/9th of the total area of a lawn. What fraction of the total area did each of them mow? - Fraction 77774

Express the value of the fraction 25/12 as a decimal number. - Birthday party

You are having a birthday party and are inviting 6 friends. You have 9 cupcakes, and you are going to share the cupcakes fairly among you and your 6 friends. How many cupcakes each friend will receive? - Why is

Why is three divided by one-fifth different from one-fifth divided by three? - Jaenette

Janette served 3/4 of a pizza to her friends. Each visitor was given 1/4 of the pizza. How many visitors shared the pizza? - Pizza 5

You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get? - Two-thirds 15

Two-thirds of a pie has already been eaten. What fraction of the pie would still leave if John ate 1/2 of what of the remaining pie? - How many 24

How many are 1/4 cup servings of raisins in 5/8 cup of raisins? - Marshall 2

Marshall Track team. After the race, the team goes to Connor's Pizza Palace. The pizza slices served at the Pizza Palace are ¼ of a whole pizza. There are 2 pizzas ready to be served. Nine students come in for lunch. Is there enough pizza for every studen - Julian 3

Julian had 7 cookie and gave half of them to a friend. How many cookies did his friend get? - A seller

A seller sliced some pizza into eights. After selling 57 slices, seven slices were left. How many whole pizzas did the vendor slice? - Divide 42

Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5)

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