# 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 2/7 * 5 1/6 = 248/21 = 11 17/21 ≅ 11.8095238

Spelled result in words is two hundred forty-eight twenty-firsts (or eleven and seventeen twenty-firsts).### How do you solve fractions step by step?

- Conversion a mixed number 2 2/7 to a improper fraction: 2 2/7 = 2 2/7 = 2 · 7 + 2/7 = 14 + 2/7 = 16/7

To find a new numerator:

a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7

b) Add the answer from previous step 14 to the numerator 2. New numerator is 14 + 2 = 16

c) Write a previous answer (new numerator 16) over the denominator 7.

Two and two sevenths is sixteen sevenths - Conversion a mixed number 5 1/6 to a improper fraction: 5 1/6 = 5 1/6 = 5 · 6 + 1/6 = 30 + 1/6 = 31/6

To find a new numerator:

a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6

b) Add the answer from previous step 30 to the numerator 1. New numerator is 30 + 1 = 31

c) Write a previous answer (new numerator 31) over the denominator 6.

Five and one sixth is thirty-one sixths - Multiple: 16/7 * 31/6 = 16 · 31/7 · 6 = 496/42 = 248 · 2/21 · 2 = 248/21

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(496, 42) = 2. In the following intermediate step, cancel by a common factor of 2 gives 248/21.

In other words - sixteen sevenths multiplied by thirty-one sixths = two hundred forty-eight twenty-firsts.

#### 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:

- 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? - Fractions

Sort fractions z_{1}= (6)/(11); z_{2}= (10)/(21); z_{3}= (19)/(22) by its size. Result write as three serial numbers 1,2,3. - A laundry

Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? - 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? - Turtles 2

A box turtle hibernates in the sand at 11 5/8. A spotted turtle hibernates at 11 16/25 feet. Which turtle is deeper? Write answer as number 1 or 2. - Math test

Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer. - Arrange

Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3 - 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 - Leo hiked

Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer? - 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? - 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? - 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?

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