Fraction calculator



This calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding fraction value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

9 2/5 ÷ 1 3/10 = 94/13 = 7 3/137.2307692

Spelled result in words is ninety-four thirteenths (or seven and three thirteenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 9 2/5 to a improper fraction: 9 2/5 = 9 2/5 = 9 · 5 + 2/5 = 45 + 2/5 = 47/5

    To find a new numerator:
    a) Multiply the whole number 9 by the denominator 5. Whole number 9 equally 9 * 5/5 = 45/5
    b) Add the answer from previous step 45 to the numerator 2. New numerator is 45 + 2 = 47
    c) Write a previous answer (new numerator 47) over the denominator 5.

    Nine and two fifths is forty-seven fifths
  2. Conversion a mixed number 1 3/10 to a improper fraction: 1 3/10 = 1 3/10 = 1 · 10 + 3/10 = 10 + 3/10 = 13/10

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 10. Whole number 1 equally 1 * 10/10 = 10/10
    b) Add the answer from previous step 10 to the numerator 3. New numerator is 10 + 3 = 13
    c) Write a previous answer (new numerator 13) over the denominator 10.

    One and three tenths is thirteen tenths
  3. Divide: 47/5 : 13/10 = 47/5 · 10/13 = 47 · 10/5 · 13 = 470/65 = 5 · 94 /5 · 13 = 94/13
    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 13/10 is 10/13) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 5 gives 94/13.
    In other words - forty-seven fifths divided by thirteen tenths = ninety-four thirteenths.




Rules for expressions with fractions:

Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, leave a space between the whole and fraction part.

Mixed numerals (mixed fractions or mixed numbers) Keep one space between the integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, use colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

Math Symbols


SymbolSymbol nameSymbol MeaningExample
+plus signaddition 1/2 + 1/3
-minus signsubtraction 1 1/2 - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate expression inside first-3/5 - (-1/4)

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.