# 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:

### - 3/8 * -4/9 = 1/6 ≅ 0.1666667

Spelled result in words is one sixth.### How do you solve fractions step by step?

- Unary minus: -3/8 = -3/8
- Multiple: the result of step No. 1 * (-4) = -3/8 * (-4) = -3 · (-4)/8 · 1 = 12/8 = 3 · 4/2 · 4 = 3/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 8) = 4. In the next intermediate step, , cancel by a common factor of 4 gives 3/2.

In words - minus three eighths multiplied by minus four = three halfs. - Divide: the result of step No. 2 : 9 = 3/2 : 9 = 3/2 · 1/9 = 3 · 1/2 · 9 = 3/18 = 3 · 1 /3 · 6 = 1/6

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 9/1 is 1/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 3 gives 1/6.

In words - three halfs divided by nine = one sixth.

#### 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:

- Length subtracting

Express in mm: 5 3/10 cm - 2/5 mm - Add sub fractions

What is 4 1/2+2/7-213/14? - School

There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males? - Fractions mul add sum

To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get? - Pizza fractions

Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left? - Cake fractions

Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others? - Difference mixed fractions

What is the difference between 4 2/3 and 3 1/6? - Mixed numbers

Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3 - Pounds

3 pounds subtract 1/3 of a pound. - Michael

Michael had a bar if chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left? - Find the 24

Find the difference between 2/7 and 1/21 - From a

From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece? - King

King had four sons. First inherit 1/2, second 1/4 , third 1/5 of property. What part of the property was left to the last of the brothers?

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