# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 2 1/4 * 1 1/2 = 27/8 = 3 3/8 = 3.375

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

- Conversion a mixed number 2 1/4 to a improper fraction: 2 1/4 = 2 1/4 = 2 · 4 + 1/4 = 8 + 1/4 = 9/4

To find a new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4

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 4.

Two and one quarter is nine quarters. - Conversion a mixed number 1 1/2 to a improper fraction: 1 1/2 = 1 1/2 = 1 · 2 + 1/2 = 2 + 1/2 = 3/2

To find a new numerator:

a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2/2 = 2/2

b) Add the answer from the previous step 2 to the numerator 1. New numerator is 2 + 1 = 3

c) Write a previous answer (new numerator 3) over the denominator 2.

One and one half is three halfs. - Multiple: 9/4 * 3/2 = 9 · 3/4 · 2 = 27/8

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(27, 8) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - nine quarters multiplied by three halfs is twenty-seven eighths.

### 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:

- Closer to one

Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B. - Place 2

Place the correct symbol, < or >, between the two numbers: 4/7? 5/6 - 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? - 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)?

- Fractions

Sort fractions z_{1}= (20)/(9); z_{2}= (10)/(21); z_{3}= (15)/(14) by their size. The result writes as three serial numbers 1,2,3. - 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? - Car crash

A car crash occurred on the road with a maximum permitted speed of 60 km/h. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, assu - 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? - Arrange

Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3

- Roma ate

Roma ate 2/5 of the cake while Somya ate 3/7 of the same cake. Who ate more, and by how much? - What 11781

What is greater: 2/5 of 10, or 20% of 4000? - Three-quarters 11361

Which is more than two-thirds of the 99 or three-quarters of the 80? - Turtles 2

A box turtle hibernates in the sand at 11 5/8 ft. A spotted turtle hibernates at 11 16/25 feet. Which turtle is deeper? Write the answer as number 1 or 2. - Torque

Torque and Mari each multiplied 1/8 inch times 5/8 inch. Tartaric 5/8 squares point inches. And Marie got 5/64 squared thought inches tall. Which student found a corrupt area?

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