# 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:

### 0.5 : 7/4 = 2/7 ≅ 0.2857143

Spelled result in words is two sevenths.### How do you solve fractions step by step?

- Conversion a decimal number to a fraction: 0.5 = 5/10 = 1/2

a) Write down the decimal 0.5 divided by 1: 0.5 = 0.5/1

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

0.5/1 = 5/10

Note: 5/10 is called a*decimal fraction*.

c) Simplify and reduce the fraction

5/10 = 1 * 5/2 * 5 = 1~~* 5~~/2~~* 5~~= 1/2 - Divide: 0.5 : 7/4 = 1/2 · 4/7 = 1 · 4/2 · 7 = 4/14 = 2 · 2 /2 · 7 = 2/7

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 7/4 is 4/7) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 2/7.

In words - one half divided by seven quarters = two 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:

- A quotient

What is the quotient of 3/10 divided by 2/4 as a fraction? - Divide 13

Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3 - Fraction of a fraction

What is two-quarters of twelve? - How many 16

How many three-tenths are there in two and one-fourths? - Monica 3

Monica works on her drawings for 2 hours. She spends 1/6 hour on each drawing. How many drawings does she work on in 2 hours? - Day

What part of the day are 23 hours 22 minutes? Express as a decimal number. - Pediatrician

Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work? - The bird

The bird feeder holds 1 and 1/2 cups of birdseed. Reagan is using a scoop that holds 1/8 of a cup. How many scoops will she need to fill the bird feeder? - Reciprocal value 2

Annabelle is making burger patties if each burger patty needs 1/16 kilogram of beef. How many patties can she make with a kilo of beef? - Volume per time 2

Benjamin drinks tea at an incredible rate. He drinks 3 1/2 liters of tea every 2/3 of an hour. Ben drinks tea at a constant rate. How much does he drink in one hour? - How many 14

How many 1/2 cup serving are in a package of cheese that contains 5 1/4 cups altogether? - The length 6

The length of 12 pipes is 10 1/2 meters. (1) find the length of one pipe (2) also find the length of 7 pipes - TV fail

The TV has after 10,000 hours average 35 failures. Determine the probability of TV failure after 400 hours of operation.

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