# Fraction calculator

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

## Result:

### 11/12 + 2 1/6 = 37/12 = 3 1/12 ≅ 3.0833333

Spelled result in words is thirty-seven twelfths (or three and one twelfth).### How do you solve fractions step by step?

- Conversion a mixed number 2 1/6 to a improper fraction: 2 1/6 = 2 1/6 = 2 · 6 + 1/6 = 12 + 1/6 = 13/6

To find a new numerator:

a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6

b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 6.

Two and one sixth is thirteen sixths - Add: 11/12 + 13/6 = 11/12 + 13 · 2/6 · 2 = 11/12 + 26/12 = 11 + 26/12 = 37/12

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(12, 6) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 6 = 72. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - eleven twelfths plus thirteen sixths = thirty-seven twelfths.

#### Rules for expressions with fractions:

**Fractions**- simply use a forward slash between the numerator and denominator, i.e., for five-hundredths, enter

**5/100**. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

**Mixed numerals**(mixed fractions or mixed numbers) write as integer separated by one space and fraction i.e.,

**1 2/3**(having the same sign). An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e.,

**1/2 : 3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

The colon

**:**and slash

**/**is the symbol of division. Can be used to divide mixed numbers

**1 2/3 : 4 3/8**or can be used for write complex fractions i.e.

**1/2 : 1/3**.

An asterisk

*****or

**×**is the symbol for multiplication.

Plus

**+**is addition, minus sign

**-**is subtraction and

**()[]**is mathematical parentheses.

The exponentiation/power symbol is

**^**- for example:

**(7/8-4/5)^2**= (7/8-4/5)

^{2}

#### 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

• exponentiation of fraction: 3/5^3

• 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

**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.

Be careful, always do

**multiplication and division**before

**addition and subtraction**. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

- Samuel

Samuel has 1/3 of a bag of rice and Isabella has a 1/2 bag of rice. What fraction of are bag of rice do they have altogether? - Adding mixed fractions

Add this two mixed numbers: 1 5/6 + 2 2/11= - Adding mixed numbers

Add this two mixed numbers: 1 5/6 + 2 2/11= - Expressions with variable

This is algebra. Let n represent an unknown number and write the following expressions: 1. 4 times the sum of 7 and the number x 2. 4 times 7 plus the number x 3. 7 less than the product of 4 and the number x 4. 7 times the quantity 4 more than the number - Roses and tulips

At the florist are 50 tulips and 5 times fewer roses. How many flowers are in the flower shop? - Lengths of the pool

Miguel swam 6 lengths of the pool. Mat swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim? - Translate 2

Translate the given phrases to mathematical phrases. Thrice the sum of three fifths and two thirds less one half is what number? - Covid-19 Pandemic

Ellice and Zia will write a research on Covid-19 Pandemic. Ellice spends 2 2/4 hours and Zia spends 3 ½ hours. How long does it take them to conduct the research for their projects? - Bus vs train

Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out? - A large 2

A large popcorn bag holds four times as much as a small popcorn bag at the end of the party 3 1/3 small bags and 2 1/4 large bags left. How many small bags with the leftover popcorn fill? - Evaluate 17

Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form. - When 5

When 5 is subtracted from both my numerator and denominator I become 3/4. What fraction i am? - Chestnuts

Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of

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