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:

1/8 + 1/2 = 5/8 = 0.625

Spelled result in words is five eighths.

How do you solve fractions step by step?

  1. Add: 1/8 + 1/2 = 1/8 + 1 · 4/2 · 4 = 1/8 + 4/8 = 1 + 4/8 = 5/8
    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(8, 2) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 2 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one eighth plus one half = five eighths.

Rules for expressions with fractions:

Fractions - simply use a forward 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 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:

  • Fraction of a fraction
    What is two-quarters of twelve?
  • Andre
    Andre, Thomas, and Ivan split 88 postage stamps in a 2:5:4 ratio. How much did Thomas get?
  • Equation with x
    Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9
  • Ratio 11
    Simplify this ratio 10 : 1/4
  • Red diplomas
    The numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase?
  • Holiday trip
    Pavel is saving for the holiday trip. He received 1100 CZK from his father. He saved a fifth himself and received the rest 500 CZK from his mother. How much did his holiday trip cost?
  • Summerjob
    Miloš saved a quarter of the money from the summerjob, bought a winter jacket for half, bought gifts for his parents and siblings for a sixth, and still had CZK 400 left. How much did Miloš earn?
  • Prospering students
    There are girls and 30 boys in the class. Boys prospering 28, girls all. How many girls are in the class and how many boys are there, if all the prospering students are 95%?
  • The perimeter 2
    The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m?
  • Dice and coin
    A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
  • Fractions mul add sum
    To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Percent calculation
    Calculate 8% if 44% is 32.
  • Red balls
    In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?


next math problems »