Calculator adding fractions and mixed numbers



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.

8/5 + 6 2/7 = 276/35 = 7 31/357.8857143

Spelled result in words is two hundred seventy-six thirty-fifths (or seven and thirty-one thirty-fifths).

How do we solve fractions step by step?

  1. Conversion a mixed number 6 2/7 to a improper fraction: 6 2/7 = 6 2/7 = 6 · 7 + 2/7 = 42 + 2/7 = 44/7

    To find a new numerator:
    a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7
    b) Add the answer from previous step 42 to the numerator 2. New numerator is 42 + 2 = 44
    c) Write a previous answer (new numerator 44) over the denominator 7.

    Six and two sevenths is forty-four sevenths
  2. Add: 8/5 + 44/7 = 8 · 7/5 · 7 + 44 · 5/7 · 5 = 56/35 + 220/35 = 56 + 220/35 = 276/35
    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(5, 7) = 35. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - eight fifths plus forty-four sevenths is two hundred seventy-six thirty-fifths.

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.