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:

7 3/10 + 9 12/15 = 171/10 = 17 1/10 = 17.1

Spelled result in words is one hundred seventy-one tenths (or seventeen and one tenth).

How do we solve fractions step by step?

  1. Conversion a mixed number 7 3/10 to a improper fraction: 7 3/10 = 7 3/10 = 7 · 10 + 3/10 = 70 + 3/10 = 73/10

    To find a new numerator:
    a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10
    b) Add the answer from previous step 70 to the numerator 3. New numerator is 70 + 3 = 73
    c) Write a previous answer (new numerator 73) over the denominator 10.

    Seven and three tenths is seventy-three tenths
  2. Conversion a mixed number 9 12/15 to a improper fraction: 9 12/15 = 9 12/15 = 9 · 15 + 12/15 = 135 + 12/15 = 147/15

    To find a new numerator:
    a) Multiply the whole number 9 by the denominator 15. Whole number 9 equally 9 * 15/15 = 135/15
    b) Add the answer from previous step 135 to the numerator 12. New numerator is 135 + 12 = 147
    c) Write a previous answer (new numerator 147) over the denominator 15.

    Nine and twelve fifteenths is one hundred forty-seven fifteenths
  3. Add: 73/10 + 147/15 = 73 · 3/10 · 3 + 147 · 2/15 · 2 = 219/30 + 294/30 = 219 + 294/30 = 513/30 = 3 · 171/3 · 10 = 171/10
    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(10, 15) = 30. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 15 = 150. In the following intermediate step, cancel by a common factor of 3 gives 171/10.
    In other words - seventy-three tenths plus one hundred forty-seven fifteenths is one hundred seventy-one tenths.

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)

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 evaluate from left to right.