# Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 1/3 * 3/5 * 2 1/4 = 9/20 = 0.45

The spelled result in words is nine twentieths.### How do we solve fractions step by step?

- Multiple: 1/3 * 3/5 = 1 · 3/3 · 5 = 3/15 = 1 · 3/5 · 3 = 1/5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 15) = 3. In the following intermediate step, cancel by a common factor of 3 gives 1/5.

In other words - one third multiplied by three fifths is one fifth. - 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. - Multiple: the result of step No. 1 * 9/4 = 1/5 * 9/4 = 1 · 9/5 · 4 = 9/20

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(9, 20) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one fifth multiplied by nine quarters is nine twentieths.

### 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

• square root of a fraction: sqrt(1/16)

• 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:

- Fractions 82848

Calculate one-seventh of the quotient of the fractions three-quarters and two-thirds. - 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. - Traveled 82609

The tourist traveled 3/8 of the planned journey on the first day and 7/12 of the trip on the second day. On which day did he travel most of the way, and by how much? - What is similar fraction

Which of the following is the similar fraction of 9/10,3/5,1/4

- 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? - One-third 6529

The worm Oliver Zoubek decided to bite through the oak log. In the first year, he made a hole in one-third. The second year, he chewed through one-third of the rest. In the third year, again, a third of the rest, and in the fourth year, he had 16 cm left. - For each

For each pair of expressions, circle the greater product without finding the product. (write 1=left expression, 2=right expression) a. 3/4 x 2/3 and 3/4 x 1/2 b. 2/3 x 3 1/4 and 4/3 x 3 1/4 c. 3/8 x 3/8 and 3/8 x 1/2

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Last Modified: October 9, 2024