# 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:

### 1/5 + 1/6 = 11/30 ≅ 0.3666667

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

- Add: 1/5 + 1/6 = 1 · 6/5 · 6 + 1 · 5/6 · 5 = 6/30 + 5/30 = 6 + 5/30 = 11/30

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 6) = 30. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 6 = 30. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - one fifth plus one sixth = eleven thirtieths.

#### 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.

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:

- Cupcakes 2

Susi has 25 cupcakes. She gives 4/5. How much does she have left? - Coal mine

The monthly plan of 17,000 tons of coal exceeded the mine by 1/25. How many tonnes of coal have been harvested from the mine above plan? - Guess a fraction

Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form) - One sixth

How many sixths are two thirds? - Playing

How long have we trained on the pitch when we know that the warm-up took 10 minutes, we trained passes for one-third of the time and we played football half the time? - Cupcakes

In a bowl was some cupcakes. Janka ate one third and Danka ate one quarter of cupcakes. a) How many of cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and in notepad also as a fraction. - PC disks

Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks? - Trip

On the trip drank 3/10 of pupils tea, 2/5 cola, 1/4 mineral water and remaining 3 juice. How many students were on the trip? - Cyclo trip

Eighth-graders took a full-day trip on a cycling course. They took 1/7 of the route to the first break and added another 3/7 of the route to lunch. They had 18 km left to the finish. How many kilometers did the trip route measure? - Comparing and sorting

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

A man spends 5/9 of his money on rent, and 5/16 of the remainder on electricity. If the final balance remaining is 550 find how much was spent on rent - Degrees Fahrenheit

C= (5)/(9)(F−32) The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I. A temperature increase of 1 degree Fahrenh - Gasoline tank 2

A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters are more needed to fill them? Show your solution.

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