# 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 5/6 - 6 1/6 = -1/3 ≅ -0.3333333

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

- Conversion a mixed number 5 5/6 to a improper fraction: 5 5/6 = 5 5/6 = 5 · 6 + 5/6 = 30 + 5/6 = 35/6

To find a new numerator:

a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6

b) Add the answer from the previous step 30 to the numerator 5. New numerator is 30 + 5 = 35

c) Write a previous answer (new numerator 35) over the denominator 6.

Five and five sixths is thirty-five sixths. - Conversion a mixed number 6 1/6 to a improper fraction: 6 1/6 = 6 1/6 = 6 · 6 + 1/6 = 36 + 1/6 = 37/6

To find a new numerator:

a) Multiply the whole number 6 by the denominator 6. Whole number 6 equally 6 * 6/6 = 36/6

b) Add the answer from the previous step 36 to the numerator 1. New numerator is 36 + 1 = 37

c) Write a previous answer (new numerator 37) over the denominator 6.

Six and one sixth is thirty-seven sixths. - Subtract: 35/6 - 37/6 = 35 - 37/6 = -2/6 = 2 · -1/2 · 3 = -1/3

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 6) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 6 = 36. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirty-five sixths minus thirty-seven sixths is minus one third.

### 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:

- Pizza 16

Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza? - Jason 3

Jason bought 3 liters of cola. He drank 3/5 liters of it and gave 2/7 liters to his brother. How much cola did Jason have left? - Benson

Benson spends ⅓ of his pocket money on transport and ⅔ on food I. What fraction of his pocket money did he spend on transport and food? ii. What fraction is left? - Nida had

Nida had 1/12 of a pizza. She gave 1/8 of it to her friend Madeeha. Find what part of the whole pizza did Madeeha get.

- In bucket

In a bucket of 87 oranges, 1/3 are spoiled, and a family member eats the remaining. How many oranges are consumed by the member of the family? - Farmer Peter

Farmer Peter paints 12 chicken coops. He started painting this day morning. He only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning? - Cups of punch

Cyka made 6 19/20 cups of punch with two different types of juice in it. If the punch had 4 1/5 cups of one type of juice, how many cups of the other type of juice did it have? - Raspberry 5406

Mom baked a raspberry pie on Saturday and divided it into 48 pieces. My father ate 2/48 cakes on the same day, Janka 4/48, and Jakub 7/48 cakes. What part of the cake remained on Sunday? - Cereals

Cole and Carl share an 18-ounce box of cereal. By the end of the week, Cole has eaten 1/6 of the box, and Carl has eaten 2/3 of the box of cereal. How many ounces are left in the box?

- There 29

There are 30 animals on the farm. 1/6 are horses, 2/5 are cows, and the rest are pigs. How many horses, cows, and pigs are there? - Carlo 2

Carlo had 5/6 of pizza, and Dannah had 1 5/8 of a similar pizza. How much more pizza did Dannah have than Carlo? - Conner

Conner picked 8 1/5 pounds of apples. Louisa picked 9 2/3 pounds of apples. How many apples, more pounds, did Louisa pick than Conner? - Canada landscape

About ½ of Canada is covered in forest, and 1/12 is covered in freshwater. What fraction of Canada is not covered in either forest or freshwater? Hint - add first and then subtract from the total. - Mother 12

Mother has 2 liters (liter=L) of milk. She used 1/8 L for making leche flan and 1/8 L for baking a cake. How much milk did she use? How much milk is left?

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