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 value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

6 + 0.413 + 0.173 = 3293/500 = 6 293/500 = 6.586

Spelled result in words is three thousand two hundred ninety-three five-hundredths (or six and two hundred ninety-three five-hundredths).

How do we solve fractions step by step?

  1. Conversion a decimal number to a fraction: 0.413 = 413/1000 = 413/1000

    a) Write down the decimal 0.413 divided by 1: 0.413 = 0.413/1
    b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
    0.413/1 = 4.13/10 = 41.3/100 = 413/1000
    Note: 413/1000 is called a decimal fraction.

    c) Simplify and reduce the fraction
    413/1000 = 413 * 1/1000 * 1 = 413 * 1/1000 * 1
  2. Add: 6 + 0.413 = 6/1 + 413/1000 = 6 · 1000/1 · 1000 + 413/1000 = 6000/1000 + 413/1000 = 6000 + 413/1000 = 6413/1000
    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(1, 1000) = 1000. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 1000 = 1000. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - six plus four hundred thirteen one-thousandths is six thousand four hundred thirteen one-thousandths.
  3. Conversion a decimal number to a fraction: 0.173 = 173/1000 = 173/1000

    a) Write down the decimal 0.173 divided by 1: 0.173 = 0.173/1
    b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
    0.173/1 = 1.73/10 = 17.3/100 = 173/1000
    Note: 173/1000 is called a decimal fraction.

    c) Simplify and reduce the fraction
    173/1000 = 173 * 1/1000 * 1 = 173 * 1/1000 * 1
  4. Add: the result of step No. 2 + 0.173 = 6413/1000 + 0.173 = 6413/1000 + 173/1000 = 6413 + 173/1000 = 6586/1000 = 2 · 3293/2 · 500 = 3293/500
    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(1000, 1000) = 1000. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1000 × 1000 = 1000000. In the following intermediate step, cancel by a common factor of 2 gives 3293/500.
    In other words - six thousand four hundred thirteen one-thousandths plus one hundred seventy-three one-thousandths is three thousand two hundred ninety-three five-hundredths.

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 use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals (mixed numbers or fractions) 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 a 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.