# 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:

### 2/3 + 5/4 = 23/12 = 1 11/12 ≅ 1.9166667

The spelled result in words is twenty-three twelfths (or one and eleven twelfths).### How do we solve fractions step by step?

- Add: 2/3 + 5/4 = 2 · 4/3 · 4 + 5 · 3/4 · 3 = 8/12 + 15/12 = 8 + 15/12 = 23/12

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, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two thirds plus five quarters is twenty-three twelfths.

### 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:

- Sum of the fractions

Find the sum, express your answer to lowest terms. 1. 1/4 + 2/4= 2. 1/6 + 3/6= 3. 6/10 + 2/10= 4. ¾ + ⅛= 5. 5 3/5 + 2 ½= - Find two 4

Find two fractions between 1/4 and 2/3. How do you know you are right? - Evaluate 33

Evaluate x+y when x=- 4/5 and y= 1/3. Write your answer as a fraction or mixed number in simplest form. - Cooking classes

Ms. Wright's two cooking classes are making a total of 60 sweet potato pies. Each pie requires 2 1/4 sweet potatoes. Her first class makes 1/3 of the total number of pies needed. Exactly how many sweet potatoes will her second class need in order to make

- Sum of AP members

Find the sum of all the numbers between 8 and 258 that are divisible by 5. - Peter 10

Peter covered 1/2 of the journey on Monday, 1/4 of the remainder on Tuesday, and the rest on Wednesday. What fraction of the journey was covered on the two days? - Add fractions

Add/subtract the following similar fraction. Express the answer in the lowest terms if possible. Write your answer inside the box: 5/12 + 6/12

more math problems »

Last Modified: October 9, 2024