# 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 1/3 - 3 5/6 = 3/2 = 1 1/2 = 1.5

The spelled result in words is three halfs (or one and one half).### How do we solve fractions step by step?

- Conversion a mixed number 5 1/3 to a improper fraction: 5 1/3 = 5 1/3 = 5 · 3 + 1/3 = 15 + 1/3 = 16/3

To find a new numerator:

a) Multiply the whole number 5 by the denominator 3. Whole number 5 equally 5 * 3/3 = 15/3

b) Add the answer from the previous step 15 to the numerator 1. New numerator is 15 + 1 = 16

c) Write a previous answer (new numerator 16) over the denominator 3.

Five and one third is sixteen thirds. - Conversion a mixed number 3 5/6 to a improper fraction: 3 5/6 = 3 5/6 = 3 · 6 + 5/6 = 18 + 5/6 = 23/6

To find a new numerator:

a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6

b) Add the answer from the previous step 18 to the numerator 5. New numerator is 18 + 5 = 23

c) Write a previous answer (new numerator 23) over the denominator 6.

Three and five sixths is twenty-three sixths. - Subtract: 16/3 - 23/6 = 16 · 2/3 · 2 - 23/6 = 32/6 - 23/6 = 32 - 23/6 = 9/6 = 3 · 3/3 · 2 = 3/2

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(3, 6) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 6 = 18. In the following intermediate step, cancel by a common factor of 3 gives 3/2.

In other words - sixteen thirds minus twenty-three sixths is three halfs.

### 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:

- A chocolate 2

A chocolate cake is cut into twelve equal pieces. Mr. Greedy eats five pieces at break time with his mug of tea. What fraction of the cake is left? - A cake

A cake has 46 slices. Harry ate 16 slices, and Jack ate 26 slices, Dave ate 0 & Mary ate 1 slice. What fraction of the cake is remaining? - You have 2

You have 6/13 of a pie. If you share 9/10, how much will you have left? - Orchard 5421

The orchard has 600 apple trees. On the first day, they cut 1/5 and 2/8 of the total number of trees on the second day. How many more trees do they have to harvest?

- 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? - Mario 4

Mario renames the mixed numbers to fractions greater than 1 to find 4 and 1/2 - 2 and 2/3. Which fractions should Mario use to find the difference? Group of answer choices - Second 82446

Petr read ⅜ of the book in the first week, ¼ of the book in the second week, and ⅒ of the book in the third week. The book has 240 pages. How many pages does Peter have left to read? - Rachel 3

Rachel has 1 cup of cinnamon. She makes cinnamon rolls from a recipe that calls for 1/8 of a cup of cinnamon per batch. If she makes 3 batches, how much cinnamon will she have left? - A recipe 5

A recipe called for 1 7/8 cups of chopped onions and 2 7/8 cups of diced spinach. How many more cups of spinach did the recipe call for?

- A football 2

A football team wins 2/5 of their matches and draws 1/3. What fraction of their matches are lost? - Bucket

Kim and Joey share a 30-ounce bucket of clay. By the end of the week, Kim has used 3/10 of the bucket. Joey has used 3/5 of the bucket of clay. How many ounces are left in the bucket? - 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 - Candy

You stop at hasty to buy candy. You give half of the bag to one friend. Then give a quarter to another friend. Later two more friends come, and you give each of them a third of what is in the bag. How many candies did you start with? - Fraction expression

Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis

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