# 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 2/7 - 4 1/3 = 20/21 ≅ 0.952381

The spelled result in words is twenty twenty-firsts.### How do we solve fractions step by step?

- Conversion a mixed number 5 2/7 to a improper fraction: 5 2/7 = 5 2/7 = 5 · 7 + 2/7 = 35 + 2/7 = 37/7

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 2. New numerator is 35 + 2 = 37

c) Write a previous answer (new numerator 37) over the denominator 7.

Five and two sevenths is thirty-seven sevenths. - Conversion a mixed number 4 1/3 to a improper fraction: 4 1/3 = 4 1/3 = 4 · 3 + 1/3 = 12 + 1/3 = 13/3

To find a new numerator:

a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3

b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 3.

Four and one third is thirteen thirds. - Subtract: 37/7 - 13/3 = 37 · 3/7 · 3 - 13 · 7/3 · 7 = 111/21 - 91/21 = 111 - 91/21 = 20/21

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 - thirty-seven sevenths minus thirteen thirds is twenty 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:

- Compare two fractions

Find which is the larger of the two fractions: 11/32, 7/24, by expressing the numbers as a) fractions with the same denominator, b) decimals. - The numerator

The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction? - Fractions 82848

Calculate one-seventh of the quotient of the fractions three-quarters and two-thirds. - 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? - Bigger 3204

How much is 1/3 bigger than 1/9? - Taylor

Taylor filled eight 5 oz glasses with orange juice ⅔ full. Emeline filled five 9 oz glasses with orange juice ¾ full. Who used more juice? - Compare fractions

Find which is the larger of the two fractions: 11/32, 7/24 by expressing the numbers as: a) fractions with the same denominator; b) decimals. - Comparing by height

Ira is 1 2/5 m tall. Her mother is 4/5 m as tall as Ira. How many times is Ira's mother taller than her?

- Percentage 63864

Through the first pipe, 90 hl of water flows into the tank per hour, and 2.7 l of water per second through the second pipe. Calculate by what percentage more or less water flows per unit time into the tank through the second pipe than through the first pi - Janet

Janet walks 7/10 miles in 1/4 hour. Ian walks 9/10 miles in 1/3 hour; who walks at the faster rate and why? - Microorganisms

The first generation of microorganisms has a population of 13500 members. Each subsequent generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation. - Order fractions

Arrange in ascending order 1 5/6, 11/9, 5/16, 3 - A laundry

Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?

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