# 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:

### 3 5/6 + 1/3 = 25/6 = 4 1/6 ≅ 4.1666667

The spelled result in words is twenty-five sixths (or four and one sixth).### How do we solve fractions step by step?

- 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 the 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. - Add: 23/6 + 1/3 = 23/6 + 1 · 2/3 · 2 = 23/6 + 2/6 = 23 + 2/6 = 25/6

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, 3) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 3 = 18. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - twenty-three sixths plus one third is twenty-five sixths.

### 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) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction

• 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:

- Balloons 2

One balloon is 3 7/10 meters above the ground. A second balloon 2 3/5 meters higher. How far above the ground is the second balloon? Complete the addition equation and a related subtraction equation to model the problem. Use x to represent the height of t - Hazelnuts 63054

Mom bought a mixture of nuts. It contains 0.2 kg of hazelnuts. 1/4 kg of cashew nuts and 2/3 kg of peanuts. How much did the whole mix weigh? - The book 4

Mr. Kinion read 3 3/4 chapters in his book on Monday. He then read 2 4/6 more chapters on Tuesday. How many chapters has he read so far? - A rope

From a rope of length 18 3/4 m, two smaller pieces of lengths 5 m and 7 1/2 m are cut out. Find the length of the remaining piece of rope.

- A baker 4

A baker has 20 cups of flour. If a loaf of bread requires 3 1/3 cups of flour and the baker made 4 loaves, how many cups of the flower were left over? - Musa worked

Musa worked for 44 hours during one five days a week. His hours are from Monday through Thursday: 3 3/4, 6 7/12, 11 5/16, and 6 5/6. Calculate the number of hours he worked on Friday. - Savings

Eva lent 1/3 of her savings to her brother, 1/2 of savings spent in the store, and 7 euros left. How much did she save? - Collected 82554

Four friends were picking apples. Filip collected 3/16, Patrik 1/4, and Tomáš 1/3 of all apples. How many apples did Štefan collect? - Rica has

Rica has 3 pieces of lace, each measuring 1/7 meter, 5/14 meter, and 3/7 meter. How long are the pieces of lace together?

- Patel

Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, 9/20 cups from the third orange, 3/11 cups from the fourth orange, and 7/15 c - Population

If 1/2 of the students are white, 1/8 of the students are latino, and 3/8 of the students are black. What percent are other? - Paul spent

Paul spent 2/5 of his money on new shirts and a ½ of his money on new shoes. What fraction of his money has been spent? What fraction is still left? - Nelly 3

Nelly jogged 7/10 km, walked 5/10 km, ran 3/10 km, walked another 7/10 km, and jogged 6/10 km. How many kilometers did she travel in all? - Flower garden

In Mr. Elliot's garden, 1/8 of the flowers are red, 1/4 of them are purple, and 1/4 of the remaining flowers are pink. If there are 128 flowers, how many of them are pink?

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