# Fraction calculator

This calculator adds two fractions. First, all fractions are converted to a common denominator when fractions have different denominators. Find the Least Common Denominator (LCD) or multiply all denominators to find a common denominator. When all denominators are the same, subtract the numerators and place the result over the common denominator. Then, simplify the result to the lowest terms or a mixed number.

## The result:

### 2/15 + 1/3 = 7/15 ≅ 0.4666667

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

- Add: 2/15 + 1/3 = 2/15 + 1 · 5/3 · 5 = 2/15 + 5/15 = 2 + 5/15 = 7/15

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(15, 3) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 3 = 45. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two fifteenths plus one third is seven 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

• 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:

- Summands 5215

Divide the number into two summands, which are in the given ratio: a) 3, 11:4 b) 5.1 8:9 c) 1 7:3 d) 0.42 1:6 - Roses and tulips

At the florist are 50 tulips and five times fewer roses. How many flowers are in the flower shop? - Arithmetic 81795

In which arithmetic sequence is S5=S6=60? - One-thirds 2485

Three classmates bought apples. Peter bought two whole one-thirds of the kg, Spring 5 sixths of a kg less than Peter and Daniel 2 times as much as Peter. How many kilograms of apples did the boys buy together?

- Rice cooking

Aunt had 1 3/4 kg of rice, then Aunt bought another 2 1/2 kg of rice, cooked 0.2 kg, calculate the remaining rice Aunt now. - Two pieces 2

Two pieces of length 12/5 m and 23/9 m are cut from a rope of length 13 m. Find the length of the remaining rope. - Master and apprentice

Master painted the roof in 3 hours and apprenticed for 4 hours. How many roofs do they paint an hour, and how many in three-quarters of an hour?

more math problems »

Last Modified: June 4, 2024