# 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:

### 3 1/2 * 3 = 21/2 = 10 1/2 = 10.5

Spelled result in words is twenty-one halfs (or ten and one half).### How do you solve fractions step by step?

- Conversion a mixed number 3 1/2 to a improper fraction: 3 1/2 = 3 1/2 = 3 · 2 + 1/2 = 6 + 1/2 = 7/2

To find a new numerator:

a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2

b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 2.

Three and one half is seven halfs - Multiple: 7/2 * 3 = 7 · 3/2 · 1 = 21/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 2) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven halfs multiplied by three = twenty-one halfs.

#### 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.

**MDAS**- Multiplication and Division have the same precedence, over Addition and Subtraction. The MDAS rule is the order of operations that are a 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:

- Dividends

The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least? - Buing

Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK? - Sandy

Sandy, John and Marg baked pies for the Bake Sale. Sandy cut his pies into 6ths, John but his into 8ths, and Marg cut hers into quarters. Sandy sold 11/6, John sold 1 3/8 pies, and Marg sold 9/4 pies. Who sold the most pies? Who sold the fewest? - Pumpkin pie

Have some pumpkin pie. One half of the pie is cut into 4 equal slices, the other half is cut into 3 equal slices. After eating one of the larger slices (on the 3 piece side), I wonder if I will eat more if I have one more from the 3 side, or two from the - Colored blocks

Tucker and his classmates placed colored blocks on a scale during a science lab. The brown block weighed 8.94 pounds, and the red block weighed 1.87 pounds. How much more did the brown block weigh than the red block? - Engineer Kažimír

The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri - Meadow

On the meadow grazing horses, cows, and sheep, together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equally. How many horses, cows, and sheep are on the meadow toget - Simplest form of a fraction

Which one of the following fraction after reducing in simplest form is not equal to 3/2? a) 15/20 b) 12/8 c) 27/18 d) 6/4 - Torque

Torque and Mari each multiplied 1/8 inch times 5/8 inch. Tartaric 5/8 squares point inches. And Marie got 5/64 squared thought inches tall. Which student found a corrupt area? - Roma ate

Roma ate 2/5 of a cake while Somya ate 3/7 of the same cake. Who ate more and by how much? - Ten fractions

Write ten fractions between 1/3 and 2/3 - Pizza palace

Josh is at Enzo's pizza palace. He can sit at a table with 5 of his friends or at a different table with seven of his friends. The same size pizza is shared equally among the people at each table. At which table should Josh sit to get more pizza? (write t - Comparing and sorting

Arrange in descending order this fractions: 2/7, 7/10 & 1/2

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