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 3/5 * 1 2/9 = 22/5 = 4 2/5 = 4.4

Spelled result in words is twenty-two fifths (or four and two fifths).

How do you solve fractions step by step?

  1. Conversion a mixed number 3 3/5 to a improper fraction: 3 3/5 = 3 3/5 = 3 · 5 + 3/5 = 15 + 3/5 = 18/5

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
    b) Add the answer from previous step 15 to the numerator 3. New numerator is 15 + 3 = 18
    c) Write a previous answer (new numerator 18) over the denominator 5.

    Three and three fifths is eighteen fifths
  2. Conversion a mixed number 1 2/9 to a improper fraction: 1 2/9 = 1 2/9 = 1 · 9 + 2/9 = 9 + 2/9 = 11/9

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/9 = 9/9
    b) Add the answer from previous step 9 to the numerator 2. New numerator is 9 + 2 = 11
    c) Write a previous answer (new numerator 11) over the denominator 9.

    One and two ninths is eleven ninths
  3. Multiple: 18/5 * 11/9 = 18 · 11/5 · 9 = 198/45 = 22 · 9/5 · 9 = 22/5
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(198, 45) = 9. In the following intermediate step, cancel by a common factor of 9 gives 22/5.
    In other words - eighteen fifths multiplied by eleven ninths = twenty-two fifths.

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:

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  • Giraffes to monkeys
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  • Stones in aquarium
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  • Sort fractions
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    compare Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3
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    kolac 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?
  • Engineer Kažimír
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  • Pizza palace
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