# 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:

### 4 - 2 2/7 = 12/7 = 1 5/7 ≅ 1.7142857

Spelled result in words is twelve sevenths (or one and five sevenths).### How do you solve fractions step by step?

- Conversion a mixed number 2 2/7 to a improper fraction: 2 2/7 = 2 2/7 = 2 · 7 + 2/7 = 14 + 2/7 = 16/7

To find new numerator:

a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7

b) Add the answer from previous step 14 to the numerator 2. New numerator is 14 + 2 = 16

c) Write a previous answer (new numerator 16) over the denominator 7.

Two and two sevenths is sixteen sevenths - Subtract: 4 - 16/7 = 4/1 - 16/7 = 4 · 7/1 · 7 - 16/7 = 28/7 - 16/7 = 28 - 16/7 = 12/7

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 the both denominators - LCM(1, 7) = 7. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 7 = 7. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - four minus sixteen sevenths = twelve sevenths.

#### Rules for expressions with fractions:

**Fractions**- use the 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 non-zero 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:

- Length subtracting

Express in mm: 5 3/10 cm - 2/5 mm - Add sub fractions

What is 4 1/2+2/7-213/14? - Pizza fractions

Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left? - School

There are 150 pupils in grade 5 . 2/3 of it are female. By what fractions are the males? - Difference mixed fractions

What is the difference between 4 2/3 and 3 1/6? - Cake fractions

Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others? - Pounds

3 pounds subtract 1/3 of a pound. - Employees

Of all 360 employees, there are 11/12 women. How many men work in a company? - Package

The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package? - Find the 24

Find the difference between 2/7 and 1/21 - Akpan

Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week? - Pupils 7

There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls? - Michael

Michael had a bar if chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?

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