# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 7 2/9 + 6 5/6 = 253/18 = 14 1/18 ≅ 14.0555556

The spelled result in words is two hundred fifty-three eighteenths (or fourteen and one eighteenth).### How do we solve fractions step by step?

- Conversion a mixed number 7 2/9 to a improper fraction: 7 2/9 = 7 2/9 = 7 · 9 + 2/9 = 63 + 2/9 = 65/9

To find a new numerator:

a) Multiply the whole number 7 by the denominator 9. Whole number 7 equally 7 * 9/9 = 63/9

b) Add the answer from the previous step 63 to the numerator 2. New numerator is 63 + 2 = 65

c) Write a previous answer (new numerator 65) over the denominator 9.

Seven and two ninths is sixty-five ninths. - Conversion a mixed number 6 5/6 to a improper fraction: 6 5/6 = 6 5/6 = 6 · 6 + 5/6 = 36 + 5/6 = 41/6

To find a new numerator:

a) Multiply the whole number 6 by the denominator 6. Whole number 6 equally 6 * 6/6 = 36/6

b) Add the answer from the previous step 36 to the numerator 5. New numerator is 36 + 5 = 41

c) Write a previous answer (new numerator 41) over the denominator 6.

Six and five sixths is forty-one sixths. - Add: 65/9 + 41/6 = 65 · 2/9 · 2 + 41 · 3/6 · 3 = 130/18 + 123/18 = 130 + 123/18 = 253/18

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(9, 6) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 6 = 54. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - sixty-five ninths plus forty-one sixths is two hundred fifty-three eighteenths.

### 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:

- Work out 2

Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - My whole

My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - Evaluate 27

Evaluate the expression shown below and write your answer as a fraction in the simplest form. (8)/(3)+ (11)/(12) - Jiwan

Jiwan Incorrectly Wrote 1+ 1/2 + 1/3 + 1/4 =1 3/9 Show The Correct Working And Write Down The Answer As A Mixed Number.

- Find two 4

Find two fractions between 1/4 and 2/3. How do you know you are right? - Drew adds

Drew adds 1/2 cup wheat flour and 2 3/4 cups white flour to his muffin batter. How many cups of flour does Drew add? - Students 82194

Out of 30 students in the class, 2 thirds of the children were on a trip, and all the others were at home. How many students stayed at home? - Evaluate 33

Evaluate x+y when x=- 4/5 and y= 1/3. Write your answer as a fraction or mixed number in simplest form. - Out of

Out of 500 oranges in a box, 3/25 are rotten, and 1/5 are kept for some guests. How many oranges are left in the box?

- Fraction multiplied by the sum

Find the three-fifths of the sum of 18 and 17. - Ben has

Ben has three rolls of border paper. Each roll has 10 4/5 feet of border. He will need 40 1/3 feet of the border for her room. How much more border does he need? - Rebecca

Rebecca needs to make a quilt. She has two pieces of fabric. One piece has 3 3/4 yards of fabric, and the other piece has 5 1/2 yards of fabric. How many yards of fabric does Rebecca currently have? - Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the numbers n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n - Administration 7994

The company RAK employs two groups of workers: workers and administration. There are three times more workers than the administration. Half of the administration and a third of the workers will be laid off. What proportion of the company's employees will

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