# 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 1/5 + 1 2/10 = 12/5 = 2 2/5 = 2.4

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

- Conversion a mixed number 1 1/5 to a improper fraction: 1 1/5 = 1 1/5 = 1 · 5 + 1/5 = 5 + 1/5 = 6/5

To find a new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5

b) Add the answer from the previous step 5 to the numerator 1. New numerator is 5 + 1 = 6

c) Write a previous answer (new numerator 6) over the denominator 5.

One and one fifth is six fifths. - Conversion a mixed number 1 2/10 to a improper fraction: 1 2/10 = 1 2/10 = 1 · 10 + 2/10 = 10 + 2/10 = 12/10

To find a new numerator:

a) Multiply the whole number 1 by the denominator 10. Whole number 1 equally 1 * 10/10 = 10/10

b) Add the answer from the previous step 10 to the numerator 2. New numerator is 10 + 2 = 12

c) Write a previous answer (new numerator 12) over the denominator 10.

One and two tenths is twelve tenths. - Add: 6/5 + 12/10 = 6 · 2/5 · 2 + 12/10 = 12/10 + 12/10 = 12 + 12/10 = 24/10 = 2 · 12/2 · 5 = 12/5

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(5, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 10 = 50. In the following intermediate step, cancel by a common factor of 2 gives 12/5.

In other words - six fifths plus twelve tenths is twelve fifths.

### 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:

- One quarter

Which of the following has a sum of 3/4? A. 1/2+1/4 B. 1/2+1/3 C. 1/4+1/8 D. 1/9+1/12 - 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? - Collected 7298

Ema collected 770 kg of waste paper during the school year, while her friend Patrik collected 15% less. During the following school year, Ema collected exactly as much as Patrik did last year, but Patrik managed to collect 15% more than Eme. Which one col - Which 10

Which will have greater momentum between a ten-wheeler truck weighing 7,000 kg and a bus that weighs 5,000kg if the bus is moving at 15 m/s while the truck is moving at 10 m/s?

- Bracelet 70684

A gold ring with a width of 1 cm is made by drilling a sphere with a radius of 1 cm through its center. A gold bracelet with a width of 1 cm is made by drilling a sphere with a radius of 4 cm through its center. Which piece of jewelry will be worth more i - Which 15

Which is larger, 1 2/7 or 10/4? - Below-average 60271

In a given group of numbers, one number is equal to the average of all, the largest number is 7 larger than the average, the smallest is 7 smaller than the average, and most numbers in the group have below-average values. What is the smallest number of nu

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Last Modified: September 8, 2024