Fraction calculator



The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

4 1/8 + 2 1/16 = 99/16 = 6 3/16 = 6.1875

Spelled result in words is ninety-nine sixteenths (or six and three sixteenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 4 1/8 to a improper fraction: 4 1/8 = 4 1/8 = 4 · 8 + 1/8 = 32 + 1/8 = 33/8

    To find new numerator:
    a) Multiply the whole number 4 by the denominator 8. Whole number 4 equally 4 * 8/8 = 32/8
    b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
    c) Write a previous answer (new numerator 33) over the denominator 8.

    Four and one eighth is thirty-three eighths
  2. Conversion a mixed number 2 1/16 to a improper fraction: 2 1/16 = 2 1/16 = 2 · 16 + 1/16 = 32 + 1/16 = 33/16

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 16. Whole number 2 equally 2 * 16/16 = 32/16
    b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
    c) Write a previous answer (new numerator 33) over the denominator 16.

    Two and one sixteenth is thirty-three sixteenths
  3. Add: 33/8 + 33/16 = 33 · 2/8 · 2 + 33/16 = 66/16 + 33/16 = 66 + 33/16 = 99/16
    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 the both denominators - LCM(8, 16) = 16. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 16 = 128. In the next intermediate step the fraction result cannot be further simplified by canceling.
    In words - thirty-three eighths plus thirty-three sixteenths = ninety-nine sixteenths.

Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2


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
• exponentiation of fraction: 3/5^3
• 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
• 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 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.
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.

Fractions in word problems:



next math problems »