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:

129/10 + 83/5 = 43/2 = 21 1/2 = 21.5

Spelled result in words is forty-three halfs (or twenty-one and one half).

How do we solve fractions step by step?

1. Conversion a mixed number 12 9/10 to a improper fraction: 12 9/10 = 12 9/10 = 12 · 10 + 9/10 = 120 + 9/10 = 129/10

To find a new numerator:
a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10/10 = 120/10
b) Add the answer from the previous step 120 to the numerator 9. New numerator is 120 + 9 = 129
c) Write a previous answer (new numerator 129) over the denominator 10.

Twelve and nine tenths is one hundred twenty-nine tenths.
2. Conversion a mixed number 8 3/5 to a improper fraction: 8 3/5 = 8 3/5 = 8 · 5 + 3/5 = 40 + 3/5 = 43/5

To find a new numerator:
a) Multiply the whole number 8 by the denominator 5. Whole number 8 equally 8 * 5/5 = 40/5
b) Add the answer from the previous step 40 to the numerator 3. New numerator is 40 + 3 = 43
c) Write a previous answer (new numerator 43) over the denominator 5.

Eight and three fifths is forty-three fifths.
3. Add: 129/10 + 43/5 = 129/10 + 43 · 2/5 · 2 = 129/10 + 86/10 = 129 + 86/10 = 215/10 = 5 · 43/5 · 2 = 43/2
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, 5) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 5 = 50. In the following intermediate step, cancel by a common factor of 5 gives 43/2.
In other words - one hundred twenty-nine tenths plus forty-three fifths is forty-three halfs.

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
-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 be evaluated from left to right.