Fraction calculator



This fraction 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.

The result:

86 14/24 + 7 13/24 = 753/8 = 94 1/8 = 94.125

The spelled result in words is seven hundred fifty-three eighths (or ninety-four and one eighth).

How do we solve fractions step by step?

  1. Conversion a mixed number 86 14/24 to a improper fraction: 86 14/24 = 86 14/24 = 86 · 24 + 14/24 = 2064 + 14/24 = 2078/24

    To find a new numerator:
    a) Multiply the whole number 86 by the denominator 24. Whole number 86 equally 86 * 24/24 = 2064/24
    b) Add the answer from the previous step 2064 to the numerator 14. New numerator is 2064 + 14 = 2078
    c) Write a previous answer (new numerator 2078) over the denominator 24.

    Eighty-six and fourteen twenty-fourths is two thousand seventy-eight twenty-fourths.
  2. Conversion a mixed number 7 13/24 to a improper fraction: 7 13/24 = 7 13/24 = 7 · 24 + 13/24 = 168 + 13/24 = 181/24

    To find a new numerator:
    a) Multiply the whole number 7 by the denominator 24. Whole number 7 equally 7 * 24/24 = 168/24
    b) Add the answer from the previous step 168 to the numerator 13. New numerator is 168 + 13 = 181
    c) Write a previous answer (new numerator 181) over the denominator 24.

    Seven and thirteen twenty-fourths is one hundred eighty-one twenty-fourths.
  3. Add: 2078/24 + 181/24 = 2078 + 181/24 = 2259/24 = 3 · 753/3 · 8 = 753/8
    It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(24, 24) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 24 × 24 = 576. In the following intermediate step, cancel by a common factor of 3 gives 753/8.
    In other words - two thousand seventy-eight twenty-fourths plus one hundred eighty-one twenty-fourths is seven hundred fifty-three eighths.




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 sign 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)

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
• reciprocal of a fraction: 1 : 3/4
• square of a fraction: 2/3^2
• cube of a fraction: 2/3^3
• exponentiation of a fraction: 1/2^4
• 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) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• 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 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 /) have the same priority and must be evaluated from left to right.

Fractions in word problems:



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