# 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:

### 1/2 * 1/2 * 1/2 * 1/2 = 1/16 = 0.0625

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

- Multiple: 1/2 * 1/2 = 1 · 1/2 · 2 = 1/4

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(1, 4) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half multiplied by one half = one quarter. - Multiple: the result of step No. 1 * 1/2 = 1/4 * 1/2 = 1 · 1/4 · 2 = 1/8

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(1, 8) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one quarter multiplied by one half = one eighth. - Multiple: the result of step No. 2 * 1/2 = 1/8 * 1/2 = 1 · 1/8 · 2 = 1/16

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(1, 16) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one eighth multiplied by one half = one sixteenth.

#### 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:

- Equation 20

In given equation: 8/9-4/5=2/9+x, find x - Integer add to fraction

7 is added to the sum of 4/5 and 6/7 - Find N 2

Find N = 1 4/5 ÷ 3/5 - Erika admin

Erika’s career consists of filing, typing and answering phones. She spends 1/6 of her time filing and 5/8 of her time typing. What fraction of her time does she spend answering phone calls? - Michael

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

3 3/4 + 2 3/5 + 5 1/2 Show your solution. - What is one third

What is 1/3 as a decimal? Give your answer rounded to 2 decimal places. - A korean

A korean mart sells banana milk, strawberry milk, and melon milk. 65% of the milks sold is banana and 14% is strawberry. What percentage is melon milk? - Tyreek

Tyreek, Antuan and Alex are given a total of $3500 to be shared among themselves in the ratio 3:5:12. How much each get money? - Orchard

3/5 of the trees in the orchard are apples, 1/3 are cherries and the remaining five trees are pear. How many trees are in the orchard? - Holiday trip

Pavel is saving for the holiday trip. He received 1100 CZK from his father. He saved a fifth himself and received the rest 500 CZK from his mother. How much did his holiday trip cost? - Calories 2

Ben eats approximately 2400 calories per day. His wife Sarah eats 5/8 as much. How many calories does Sarah eat per day? - Visit to grandfather

Shane's family traveled 3/10 of the distance to his grandfather’s house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his grandfather’s house was traveled on Sunday?

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