# 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 6/7 - 2 2/3 = 67/21 = 3 4/21 ≅ 3.1904762

The spelled result in words is sixty-seven twenty-firsts (or three and four twenty-firsts).### How do we solve fractions step by step?

- Conversion a mixed number 5 6/7 to a improper fraction: 5 6/7 = 5 6/7 = 5 · 7 + 6/7 = 35 + 6/7 = 41/7

To find a new numerator:

a) Multiply the whole number 5 by the denominator 7. Whole number 5 equally 5 * 7/7 = 35/7

b) Add the answer from the previous step 35 to the numerator 6. New numerator is 35 + 6 = 41

c) Write a previous answer (new numerator 41) over the denominator 7.

Five and six sevenths is forty-one sevenths. - Conversion a mixed number 2 2/3 to a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3

To find a new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write a previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds. - Subtract: 41/7 - 8/3 = 41 · 3/7 · 3 - 8 · 7/3 · 7 = 123/21 - 56/21 = 123 - 56/21 = 67/21

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(7, 3) = 21. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - forty-one sevenths minus eight thirds is sixty-seven twenty-firsts.

### 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:

- Which 15

Which is larger, 1 2/7 or 10/4? - Equivalent fractions

Are these two fractions -4/9 and 11/15 equivalent? - Tourists 82400

On the first day, tourists covered 3/14 of the planned route, on the second day 1/3 of the route, and on the third day 8/21 of the route. On which day did they walk the longest part of the route (1,2,3)? - Andy and Mike

Mike and Andy are each reading the same book. Mike read 2/4 of the book on Tuesday and 1/3 of the book on Wednesday. Andy read 1/2 of the book on Tuesday and 1/5 of the book on Wednesday. Andy says that altogether he read more of the book on Tuesday and W

- One quarter

Which of the following has a sum of 3/4? A. 1/2+1/4 B. 1/2+1/3 C. 1/4+1/8 D. 1/9+1/12 - An Airbus

An Airbus A380 has one first-class section, one business-class section, and 4 economy-class sections. The first-class section of the Airbus A380 has 14 seats, 5/7 are being used. The business-class section has 64 seats. 5/16 is being used. Each Economy-cl - 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? - True or false?

Which of the following is true? A. Three and three ninths plus seven and six-elevenths equal ten and eighty-seven ninety ninths. B. two and three-eighths plus six and four-fifths equals eight and twelve fortieth C. three and three sevenths plus four and t - Colored blocks

Tucker and his classmates placed colored blocks on a scale during a science lab. The brown block weighed 8.94 pounds, and the red block weighed 1.87 pounds. How much more did the brown block weigh than the red block?

- How many

How many integers are greater than 547/3 and less than 931/4? - Calculate 26051

The base of the prism has the shape of a square with a side of 10 cm. The height of the prism is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume. - Anesa

Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - Ten fractions

Write ten fractions between 1/3 and 2/3 - Fractions 3928

Arrange the fractions from the smallest to the largest. 2/5, 15/6, 1/4, 5/5, 5/4, 4/10, 6/5.

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