# 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:

### 2 4/18 + 6/18 = 23/9 = 2 5/9 ≅ 2.5555556

Spelled result in words is twenty-three ninths (or two and five ninths).### How do you solve fractions step by step?

- Conversion a mixed number 2 4/18 to a improper fraction: 2 4/18 = 2 4/18 = 2 · 18 + 4/18 = 36 + 4/18 = 40/18

To find a new numerator:

a) Multiply the whole number 2 by the denominator 18. Whole number 2 equally 2 * 18/18 = 36/18

b) Add the answer from previous step 36 to the numerator 4. New numerator is 36 + 4 = 40

c) Write a previous answer (new numerator 40) over the denominator 18.

Two and four eighteenths is forty eighteenths - Add: 40/18 + 6/18 = 40 + 6/18 = 46/18 = 2 · 23/2 · 9 = 23/9

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(18, 18) = 18. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 18 × 18 = 324. In the following intermediate step, cancel by a common factor of 2 gives 23/9.

In other words - forty eighteenths plus six eighteenths = twenty-three ninths.

#### 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:

- Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the number 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 - Fe metal sheet

For one product, 5/8 of the metal sheet are consumed, to the second 5/6 of remains. What part of the sheet metal is consumed for both products together? - Simplify 3

Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution. - Add two fractions

What is the sum of 2/3 and 3/10? - Adding mixed fractions

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

One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all? - A market

A market vendor was able to sell all the mangoes, papayas, and star apples. 1/5 of the fruits were mangoes, 2/3 of them were papayas and the rest were star apples. How many parts of the fruits sold are star apples? - Adding mixed numbers

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

During a visit to an orchard, Greg picked 3/5 of a bag of delicious golden apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in t - Circular garden

Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante - Adding mixed 4

2 and 1/8th plus 1 and 1/3rd = - Roses and tulips

At the florist are 50 tulips and 5 times fewer roses. How many flowers are in the flower shop? - Honey 3

Honey jogged 1 3/4 km on Monday,1 1/2 km on Wednesday and 1 2/3 km on Friday . how far did he jog?

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