# 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 1/2) : (1/4) = 10/1 = 10

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

- Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs - Divide: 5/2 : 1/4 = 5/2 · 4/1 = 5 · 4/2 · 1 = 20/2 = 2 · 10 /2 · 1 = 10

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 1/4 is 4/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 10/1.

In other words - five halfs divided by one quarter = ten.

#### 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

**the 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.

**MDAS**- Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.

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:

- Pie division

5/8 of a pie divide 6 pieces. Each friend got 1/6. What fraction of the whole pie does each person receive? - 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 - Lemonade 4

Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get? - Reciprocal of mixed number

Find the reciprocal of 1 2/5. - Find N 2

Find N = 1 4/5 ÷ 3/5 - Fraction of a fraction

What is two-quarters of twelve? - Pechay

Jan has 3/8 kilogram of pechay. If he will share 1/8 kilogram to each of his friends, how many of his friends can receive the pechay? - How many 16

How many three-tenths are there in two and one-fourths? - Evaluate 12

Evaluate and simplify 9 divided by 7/6. - Percent calculation

Calculate 8% if 44% is 32. - The physical

The physical therapist asks Mr. Smith to walk 20 minutes in one hour to improve his ambulation. What fractional part of an hour is Mr. Smith to exercise? - Nicola 2

Nicola is playing a video game where each round lasts 7/12 of an hour. She has scheduled 3 3/4 hours to play the game. How many rounds can Nicole play?

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