# 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:

### 2 1/3 + 3 1/2 = 35/6 = 5 5/6 ≅ 5.8333333

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

- Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

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 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds. - Conversion a mixed number 3 1/2 to a improper fraction: 3 1/2 = 3 1/2 = 3 · 2 + 1/2 = 6 + 1/2 = 7/2

To find a new numerator:

a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2

b) Add the answer from the previous step 6 to the numerator 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 2.

Three and one half is seven halfs. - Add: 7/3 + 7/2 = 7 · 2/3 · 2 + 7 · 3/2 · 3 = 14/6 + 21/6 = 14 + 21/6 = 35/6

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(3, 2) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 2 = 6. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven thirds plus seven halfs is thirty-five sixths.

### 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:

- Add two fractions

What is the sum of 2/3 and 3/10? - Matthew

Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far? - Mary spent

Mary spent 3/4 hour doing science and 1/8 hour reading. How much time did she spend studying? - Rachel 2

Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?

- A biology

A biology experiment required pouring 2/9 liter of nutrient solution and 2/3 liter of pure water into a tank. At the end of the experiment, 3/10 liter of fluid had evaporated. How much fluid was left in the tank? - Paul spent

Paul spent 2/5 of his money on new shirts and a ½ of his money on new shoes. What fraction of his money has been spent? What fraction is still left? - Wednesday 67114

Emil and Erika are playing a board game. a) on Monday, they started playing at 17:36 and played for 45 minutes. What time was it when they finished? b) on Tuesday, they played from 4:47 p.m. Until half past six. How many minutes did they play? c) they pla - Product and sum

What is the product of two-fourths and the sum of three halves and four? - A basket 2

A basket contains three types of fruits weighing 87/4 kg in all. If 23/4 kilograms of these are oranges, 48/7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket?

- Math homework

It took Jose two-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, and any two-fifths of an hour on Wednesday. How many hours did it take Jose to complete his homework altogether? - Series and sequences

Find a fraction equivalent to the recurring decimal. 0.435643564356 - Use AP sum formula

If x+3x+5x+7x+...+87x=5808, what is the value of x? - A rope

From a rope of length 18 3/4 m, two smaller pieces of lengths 5 m and 7 1/2 m are cut out. Find the length of the remaining piece of rope. - The mall

Pia spent 1 9/12 hours in her grandparents' house. This time was 8/12 of an hour more than the time she spent at the mall. How much time did she spend at the mall?

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