# 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:

### 4/5 * 2 2/3 = 32/15 = 2 2/15 ≅ 2.1333333

The spelled result in words is thirty-two fifteenths (or two and two fifteenths).### How do we solve fractions step by step?

- 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. - Multiple: 4/5 * 8/3 = 4 · 8/5 · 3 = 32/15

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(32, 15) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - four fifths multiplied by eight thirds is thirty-two fifteenths.

### 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:

- Playing games

In a school, 9/10 of the students take part. 2/3 of these play football. What fraction of the students play football? - The cost 7

The cost of a pen is Rs. 20/3, and that of a pencil is 25/6. Which costs more and by how much? - Four children

Father saved a certain amount of money in the bank. He divided this amount equally among his four children. One of the daughters donated 3/7 of the amount she received to her son and 4/9 of it to her daughter. What part of the total amount saved did the s - Dividends

The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?

- Choose

Choose the three equivalent forms of 6.375. A. six and three eighths, 6.375%, fifty one eighths B. six and three seventy fifths, 6.375%, thirty seven sixths C. six and three seventy fifths, 637.5%, thirty seven sixths D. six and three eighths, 637.5%, fif - Sandy

Sandy, John, and Marg baked pies for the Bake Sale. Sandy cut his pies into 6ths, John cut his into 8ths, and Marg cut hers into quarters. Sandy sold 11/6, John sold 1 3/8 pies, and Marg sold 9/4 pies. Who sold the most pies? Who sold the fewest? - Children 35891

Three children got part of the cake. Which got the most? Tomas 24% Lenka 0.3 Philip 2/7 - Equivalent expressions

A coach took his team out for pizza after their last game. There were 14 players, so they had to sit in smaller groups at different tables. Six players sat at one table and got four small pizzas to share equally. The other players sat at a different table - Which 15

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

- Parul

Parul and Tarun ran a race of 200m. Parul completed the race in 2/3 min and Taun in 3/5 mins. Who took more time? - What 11781

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

Ricardo is 1 9/10 metres tall. If Ricardo is 3/10 meters taller than Joan, what is Joan's height in meters? - Place 2

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

Which of the following fractions is the largest? 29/36 5/6 7/9 3/4

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