# Fraction calculator

## Result:

### (1/12) : (1/4) = 13 ≅ 0.3333333

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

- Divide: 112 : 14 = 112 · 41 = 1 · 412 · 1 = 412 = 4 · 1 4 · 3 = 13

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 14 is 41) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step cancelling by a common factor of 4 gives 13.

In words - one twelfth divided by one quarter = one third.

#### 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 number 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 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**.

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

Calculator follows well-known rules for

**order of operations**. 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:

- Video game

Nicole 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? - Reminder and quotient

There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1, - Bonus

Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses? - Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane. - Two divided

Two divided by nine tenths. - Cake 7

1/3 of a cake shared with 4 people. What share of the whole cake has each people? - Sewing

Beth's mother can sew 235 pairs of short pants in 6 days while Lourdes can sew 187 pairs in 8 days. How many more pairs of short pants can Beth's mother sew? - Day

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

We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2? - Chicks

How many chicks were hatched from 4500 eggs, when an average of 100 eggs hatched 87 chicks? - Diophantus

We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth - Unit rate

Find unit rate: 6,840 customers in 45 days - Pediatrician

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

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