# 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:

### 3 1/4 + 3 5/8 = 55/8 = 6 7/8 = 6.875

The spelled result in words is fifty-five eighths (or six and seven eighths).### How do we solve fractions step by step?

- Conversion a mixed number 3 1/4 to a improper fraction: 3 1/4 = 3 1/4 = 3 · 4 + 1/4 = 12 + 1/4 = 13/4

To find a new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4

b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 4.

Three and one quarter is thirteen quarters. - Conversion a mixed number 3 5/8 to a improper fraction: 3 5/8 = 3 5/8 = 3 · 8 + 5/8 = 24 + 5/8 = 29/8

To find a new numerator:

a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8

b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29

c) Write a previous answer (new numerator 29) over the denominator 8.

Three and five eighths is twenty-nine eighths. - Add: 13/4 + 29/8 = 13 · 2/4 · 2 + 29/8 = 26/8 + 29/8 = 26 + 29/8 = 55/8

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(4, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirteen quarters plus twenty-nine eighths is fifty-five eighths.

### 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:

- A farmer 9

A farmer has 3 hectares of an orchard. ½ of the land is occupied by apples, ⅙ of the remainder is occupied by lemon trees, and tree tomatoes occupy the rest of it. Find the fraction of the land occupied by tree tomatoes. - A bakery

A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one-fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equa - Sequence 80450

How many terms does the sequence have if a1=4, Sn=589, d=3, n=? - Sum of three fractions

What is the sum of 6/7, 1/2 & 3/4?

- Integer add to fraction

Seven is added to the sum of 4/5 and 6/7 - 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 dump

A dump truck bought 1/3 of a ton of rock on the first trip, 1/2 of a ton on the second trip, and 4/5 of a ton on the third trip. What was the total weight of the rock?

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Last Modified: October 9, 2024