# 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:

### 1/4 + 1/4 + 1/4 = 3/4 = 0.75

Spelled result in words is three quarters.### How do you solve fractions step by step?

- Add: 1/4 + 1/4 = 1 + 1/4 = 2/4 = 2 · 1/2 · 2 = 1/2

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(4, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 4 = 16. In the following intermediate step, cancel by a common factor of 2 gives 1/2.

In other words - one quarter plus one quarter = one half. - Add: the result of step No. 1 + 1/4 = 1/2 + 1/4 = 1 · 2/2 · 2 + 1/4 = 2/4 + 1/4 = 2 + 1/4 = 3/4

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(2, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half plus one quarter = three quarters.

#### 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

**the 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 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:

- Unknown number

I think the number - its sixth is 3 smaller than its third. - Cakes

On the bowl were a few cakes. Jane ate one-third of them, and Dana ate a quarter of those cakes that remained. a) What part (of the original number of cakes) Dana ate? b) At least how many cakes could be (initially) on the bowl? - Farmers 2

On Wednesday the farmers at the Grant Farm picked 2 barrels of tomatoes. Thursday, the farmers picked 1/2 as many tomatoes as on Wednesday. How many barrels of tomatoes did the farmers pick on Thursday? - Cupcakes 2

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

One evening 2/3 of students watch TV. Of those students, 3/8 watched a reality show. Of the students that watched the show, 1/4 of them recorded it. What fraction of the students watched and recorded reality tv. - Write 3

Write a real-world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10, then solve the problem. - Equation with fractions

Solve an equation: 1- (2x-5)/(6) =3- (x)/(4) It is an equation with fractions. - Unknown number 6

Determine the unknown number, which is by 1.5 greater than its fourth. - Percentages

What is 1/3 of $821.43? - Missing number

Blank +1/6 =3/2 find the missing number - Tank 11

When 150 litres has been drawn from a tank it is 3/8 full, how many litres will the tank hold? - UN 1

If we add to an unknown number his quarter, we get 210. Identify unknown number. - 3 children

3 children had to divide 4 pounds is candy. How much candy did each child get?

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