# 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:

### 1 1/3 * 1 4/9 = 52/27 = 1 25/27 ≅ 1.9259259

The spelled result in words is fifty-two twenty-sevenths (or one and twenty-five twenty-sevenths).### How do we solve fractions step by step?

- Conversion a mixed number 1 1/3 to a improper fraction: 1 1/3 = 1 1/3 = 1 · 3 + 1/3 = 3 + 1/3 = 4/3

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3

b) Add the answer from the previous step 3 to the numerator 1. New numerator is 3 + 1 = 4

c) Write a previous answer (new numerator 4) over the denominator 3.

One and one third is four thirds. - Conversion a mixed number 1 4/9 to a improper fraction: 1 4/9 = 1 4/9 = 1 · 9 + 4/9 = 9 + 4/9 = 13/9

To find a new numerator:

a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/9 = 9/9

b) Add the answer from the previous step 9 to the numerator 4. New numerator is 9 + 4 = 13

c) Write a previous answer (new numerator 13) over the denominator 9.

One and four ninths is thirteen ninths. - Multiple: 4/3 * 13/9 = 4 · 13/3 · 9 = 52/27

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(52, 27) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - four thirds multiplied by thirteen ninths is fifty-two twenty-sevenths.

### 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. - Same fractions

I remember that 2/2 is equal to 1. 3/3 is equal to 1. Where is the fraction 4/4 located on the number line? - Fractions 82848

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

- Comparing and sorting

Arrange in descending order these fractions: 2/7, 7/10 & 1/2 - 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. - The correct

The correct missing numerator in 2/4 = _/8 to make the fraction equal is - Sort fractions

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

- 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? - Three-quarters 11361

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

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