# 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:

### (1 1/8) : 2 = 9/16 = 0.5625

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

- Conversion a mixed number 1 1/8 to a improper fraction: 1 1/8 = 1 1/8 = 1 · 8 + 1/8 = 8 + 1/8 = 9/8

To find a new numerator:

a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8

b) Add the answer from the previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 8.

One and one eighth is nine eighths. - Divide: 9/8 : 2 = 9/8 · 1/2 = 9 · 1/8 · 2 = 9/16

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 2/1 is 1/2) 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 - nine eighths divided by two is nine sixteenths.

### 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:

- Divide 42

Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5) - Two boxes 3

Two boxes of pizza of the same size are left on the table. One box has 1/2 of a pizza, and the other has 3/4 of a pizza left in it. Then, Mother divides all the pizzas into 1/8 each. How many were many slices of pizza left? - 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? - Robotics team

The 4 robotics team members held a car wash to raise money. To attract customers, each person held a sign by the road for an equal portion of the car wash, which lasted 3 hours in all. How long did each person hold the sign?

- They brought

They brought 180 kg of grapes to the market. They sold 72 kg of them. What part of the grapes did they sell? - What 82170

What part of €24 is €12, €4, €8, €1, €18, €20? - Expression with powers

Which expression is equivalent to 2.1 raised to the fifth power divided by 0.9 raised to the fourth power, all raised to the third power? - A pizza 3

A pizza shop charges $2.00 for a slice that is one-eighth of a pizza and $3.00 for a slice that is one-fourth of a pizza. One day the pizza shop makes six pizzas. How much more money will they make if they slice all the pizzas into eighths than if they sl - 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?

- Six friends

Six friends who live inland decide to take a road trip to the closest beach, which is 661 1/2 kilometers away. They decided to share the driving equally. How many kilometers will each person have to drive - 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? - A rope cut

From a rope of 200 m, pieces of equal sizes are cut. If each part is ¼ m, find the number of pieces. - Jana mixing

Jana mix is 1/4 gallon of orange juice and 1/2 gallon of pineapple juice to make punch. Each serving is 1/16 gallon. How many servings can go in? Make sure you work. - Calculate 68454

Calculate how many times the square of the number 1/100 is less than 1/1000. (numbers in fraction form)

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