# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 9 1/8 - 3 5/6 = 127/24 = 5 7/24 ≅ 5.2916667

Spelled result in words is one hundred twenty-seven twenty-fourths (or five and seven twenty-fourths).### How do we solve fractions step by step?

- Conversion a mixed number 9 1/8 to a improper fraction: 9 1/8 = 9 1/8 = 9 · 8 + 1/8 = 72 + 1/8 = 73/8

To find a new numerator:

a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/8 = 72/8

b) Add the answer from previous step 72 to the numerator 1. New numerator is 72 + 1 = 73

c) Write a previous answer (new numerator 73) over the denominator 8.

Nine and one eighth is seventy-three eighths - Conversion a mixed number 3 5/6 to a improper fraction: 3 5/6 = 3 5/6 = 3 · 6 + 5/6 = 18 + 5/6 = 23/6

To find a new numerator:

a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6

b) Add the answer from previous step 18 to the numerator 5. New numerator is 18 + 5 = 23

c) Write a previous answer (new numerator 23) over the denominator 6.

Three and five sixths is twenty-three sixths - Subtract: 73/8 - 23/6 = 73 · 3/8 · 3 - 23 · 4/6 · 4 = 219/24 - 92/24 = 219 - 92/24 = 127/24

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

In other words - seventy-three eighths minus twenty-three sixths is one hundred twenty-seven 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

• multiplying a fraction by a whole number: 6 * 3/4

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• 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 evaluate from left to right.

## Fractions in word problems:

- Peter's calculation

Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - Bucket

Kim and Joey share a 30-ounce bucket of clay. By the end of the week, Kim has used 3/10 of the bucket. Joey has used 3/5 of the bucket of clay. How many ounces are left in the bucket? - Paul ate

Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents? - You have 2

You have 6/13 of a pie. If you share 9/10, how much will you have left? - King

King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers? - Difference between fractions

What is the difference when you take away 1/6 from 2/8? - Flags 2

1/4 are white and another 1/4 are yellow. What fraction of the flags are either white or yellow? - Mr. Vandar

Mr. Vandar washed 1/4 of his laundry. His son washed 2/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? - The entity

What is the difference between seven-tenths of an entity and seven-fifteenths of the same entity? Please solve it for me. - The bread 2

Sandra and Tylar baked two loaves of bread. On Monday, they ate 1/2 of one loaf. On Tuesday, they ate 1/3 of one loaf of bread. How much bread is left? - Sundar

Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and ate 1/5 of them. How many chocolates are left with Sundar?

more math problems »