Calculator adding fractions and mixed numbers



This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.

8/5 + 6 2/7 = 276/35 = 7 31/35 ≅ 7.8857143

The result spelled out 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 the 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
    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(5, 7) = 35. 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 equals two hundred seventy-six thirty-fifths.

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . 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 are:
  • PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
  • BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
  • BODMAS: Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction.
  • GEMDAS: Grouping symbols (brackets: `(){}`), Exponents, Multiplication, Division, Addition, Subtraction.
  • MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.
Important Notes:
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., `+` and `-`, or `*` and `/`) must be evaluated from left to right.

Fractions in word problems:



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Last Modified: March 25, 2025