# 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:

### (3/4) : (5 1/5) = 15/104 ≅ 0.1442308

Spelled result in words is fifteen one-hundred fourths.### How do you solve fractions step by step?

- Conversion a mixed number 5 1/5 to a improper fraction: 5 1/5 = 5 1/5 = 5 · 5 + 1/5 = 25 + 1/5 = 26/5

To find a new numerator:

a) Multiply the whole number 5 by the denominator 5. Whole number 5 equally 5 * 5/5 = 25/5

b) Add the answer from previous step 25 to the numerator 1. New numerator is 25 + 1 = 26

c) Write a previous answer (new numerator 26) over the denominator 5.

Five and one fifth is twenty-six fifths - Divide: 3/4 : 26/5 = 3/4 · 5/26 = 3 · 5/4 · 26 = 15/104

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 26/5 is 5/26) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - three quarters divided by twenty-six fifths = fifteen one-hundred fourths.

#### 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:

- Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n - The third

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Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes? - Almonds

Rudi has 4 cups of almonds. His trail mix recipe calls for 2/3 cup of almonds. How many batches of trail mix can he make? - Sir Toffie

One hot afternoon, Sir Toffie went to his backyard to plant monggo. In his seed box, he found out that different seeds like monggo, pechay, eggplant, and tomatoes were accidentally mixed because of the strong wind. He sieved the mixed seeds and was able t - The balls

You have 108 red and 180 green balls. You have to be grouped into the bags so that the ratio of red to green in each bag was the same. What smallest number of balls may be in one bag? - The floor

The floor collapsed because three and a half times the amount it had been designed to hold had been stored in the room. If 980 tons had been stored in the room, what amount was the floor designed to hold? - Cube in a sphere

The cube is inscribed in a sphere with a volume 7253 cm^{3}. Determine the length of the edges of a cube. - Pizza 5

You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get? - Ten fractions

Write ten fractions between 1/3 and 2/3 - Percent calculation

Calculate 8% if 44% is 32. - Composite ratio

Jakub, Aneta, and Lenka divided 1342 USD in the ratio 5/2: 3/10: 1/4. How much did Lenka take?

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