# 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:

### (1/8) : 2 = 1/16 = 0.0625

Spelled result in words is one sixteenth.### How do you solve fractions step by step?

- Divide: 1/8 : 2 = 1/8 · 1/2 = 1 · 1/8 · 2 = 1/16

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 2/1 is 1/2) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - one eighth divided by two = one sixteenth.

#### 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? - Fraction of a fraction

What is two-quarters of twelve? - 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? - 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? - TV fail

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

Jerry has 3/4 of a pizza. He needs to share it with 6 friends. What fraction of the pizza will each friend get? Only write the fraction - Split between 4

There are 12 1/4 pounds of candy canes to split between four classes evenly. How many pounds of the candy canes will each class get? - Prime divisors

Find 2/3 of the sum's ratio and the product of all prime divisors of the number 120. - Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1. - Lemonade

How many 1/4 cup servings are in 2 and 1/3 cups of lemonade? - Third of an hour

How many minutes is a third of an hour? Do you know to determine a third of the lesson hour (45min)?

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