# Fraction calculator

This fraction 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 1/6 * 6 3/4 = 63/8 = 7 7/8 = 7.875

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

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

To find a new numerator:

a) Multiply the whole number 1 by the denominator 6. Whole number 1 equally 1 * 6/6 = 6/6

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 6.

One and one sixth is seven sixths. - Conversion a mixed number 6 3/4 to a improper fraction: 6 3/4 = 6 3/4 = 6 · 4 + 3/4 = 24 + 3/4 = 27/4

To find a new numerator:

a) Multiply the whole number 6 by the denominator 4. Whole number 6 equally 6 * 4/4 = 24/4

b) Add the answer from the previous step 24 to the numerator 3. New numerator is 24 + 3 = 27

c) Write a previous answer (new numerator 27) over the denominator 4.

Six and three quarters is twenty-seven quarters. - Multiple: 7/6 * 27/4 = 7 · 27/6 · 4 = 189/24 = 63 · 3/8 · 3 = 63/8

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(189, 24) = 3. In the following intermediate step, cancel by a common factor of 3 gives 63/8.

In other words - seven sixths multiplied by twenty-seven quarters is sixty-three 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:

- Pizza 16

Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza? - Carlo 2

Carlo had 5/6 of pizza, and Dannah had 1 5/8 of a similar pizza. How much more pizza did Dannah have than Carlo? - Once simplified

Once simplified, which of the expressions below have a value between 20 and 30? Select all that apply. A) 32÷8×514 B) -18÷6×9 C) 4×12÷2 D) 12×413÷(-2) - Conner

Conner picked 8 1/5 pounds of apples. Louisa picked 9 2/3 pounds of apples. How many apples, more pounds, did Louisa pick than Conner?

- Compare fractions

Find which is the larger of the two fractions: 11/32, 7/24 by expressing the numbers as: a) fractions with the same denominator; b) decimals. - Achievement 66164

The test consisted of 50 questions, each with one possible correct answer. The test result is given by the sum of the correct answers, a maximum of 100 points. The criterion for admission was the achievement of 50 points. The study applicant answered 36 q - Sort fractions

Which of the following fractions is the largest? 29/36 5/6 7/9 3/4

more math problems »

Last Modified: August 30, 2024