# 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:

### 7 1/6 - 3 5/8 = 85/24 = 3 13/24 ≅ 3.5416667

The spelled result in words is eighty-five twenty-fourths (or three and thirteen twenty-fourths).### How do we solve fractions step by step?

- Conversion a mixed number 7 1/6 to a improper fraction: 7 1/6 = 7 1/6 = 7 · 6 + 1/6 = 42 + 1/6 = 43/6

To find a new numerator:

a) Multiply the whole number 7 by the denominator 6. Whole number 7 equally 7 * 6/6 = 42/6

b) Add the answer from the previous step 42 to the numerator 1. New numerator is 42 + 1 = 43

c) Write a previous answer (new numerator 43) over the denominator 6.

Seven and one sixth is forty-three sixths. - 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. - Subtract: 43/6 - 29/8 = 43 · 4/6 · 4 - 29 · 3/8 · 3 = 172/24 - 87/24 = 172 - 87/24 = 85/24

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(6, 8) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 8 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - forty-three sixths minus twenty-nine eighths is eighty-five twenty-fourths.

### 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:

- Fraction operations

For items - fractions 1/6 - 1/9 perform the indicated operation/s. Write your answer in improper fractions, and it must be in the simplest form. - The cat

The cat starts with 4/6 of a cup in his bowl. It eats 1/4 of a cup of food. How much food is left? - Marbles 82374

How many marbles do I have if I am missing a fifth of 15 marbles? - You have 4

You have eaten ⅔ of a pizza. Your friend eats what is left. How much of the original pizza is left?

- Fraction subtraction

Find the difference. Reduce the answer to the simplest form: 1.) ¾ - 1/8 = 2.) ½ - 1/8 = 3.) ½ - 1/6 = 4.) 7/8 - ¾ = 5.) 1/5 - 1/10 - Subtract 19

Subtract as indicated. 11/10 - (- 2/5) - Evaluate 38

Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(6) - (3)/(8) Transcription: start fraction, 5, divided by, 6, end fraction, minus, start fraction, 3, divided by, 8, end fraction

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Last Modified: October 9, 2024