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:

5 5/7 * 3 1/8 = 125/7 = 17 6/717.8571429

Spelled result in words is one hundred twenty-five sevenths (or seventeen and six sevenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 5 5/7 to a improper fraction: 5 5/7 = 5 5/7 = 5 · 7 + 5/7 = 35 + 5/7 = 40/7

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 7. Whole number 5 equally 5 * 7/7 = 35/7
    b) Add the answer from previous step 35 to the numerator 5. New numerator is 35 + 5 = 40
    c) Write a previous answer (new numerator 40) over the denominator 7.

    Five and five sevenths is forty sevenths
  2. Conversion a mixed number 3 1/8 to a improper fraction: 3 1/8 = 3 1/8 = 3 · 8 + 1/8 = 24 + 1/8 = 25/8

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8
    b) Add the answer from previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
    c) Write a previous answer (new numerator 25) over the denominator 8.

    Three and one eighth is twenty-five eighths
  3. Multiple: 40/7 * 25/8 = 40 · 25/7 · 8 = 1000/56 = 125 · 8/7 · 8 = 125/7
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(1000, 56) = 8. In the following intermediate step, cancel by a common factor of 8 gives 125/7.
    In other words - forty sevenths multiplied by twenty-five eighths = one hundred twenty-five sevenths.

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:

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  • Math test
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  • Comparing and sorting
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  • Arrange
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  • Compare
    Compare fractions (34)/(3) and (12)/(4). Which fraction of the lower?
  • Stones in aquarium
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