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:

2 1/3 * 3 1/2 = 49/6 = 8 1/68.1666667

Spelled result in words is forty-nine sixths (or eight and one sixth).

How do you solve fractions step by step?

  1. Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
    b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
    c) Write a previous answer (new numerator 7) over the denominator 3.

    Two and one third is seven thirds
  2. Conversion a mixed number 3 1/2 to a improper fraction: 3 1/2 = 3 1/2 = 3 · 2 + 1/2 = 6 + 1/2 = 7/2

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2
    b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
    c) Write a previous answer (new numerator 7) over the denominator 2.

    Three and one half is seven halfs
  3. Multiple: 7/3 * 7/2 = 7 · 7/3 · 2 = 49/6
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(49, 6) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - seven thirds multiplied by seven halfs = forty-nine sixths.

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:

  • Pizza palace
    Josh is at Enzo's pizza palace. He can sit at a table with 5 of his friends or at a different table with seven of his friends. The same size pizza is shared equally among the people at each table. At which table should Josh sit to get more pizza? (write t
  • Arrange
    Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3
  • Equivalent expressions
    A coach took his team out for pizza after their last game. There were 14 players, so they had to sit in smaller groups at different tables. Six players sat at one table and got 4 small pizzas to share equally. The other players sat at the different table
  • How many
    How many integers are greater than 547/3 and less than 931/4?
  • Leo hiked
    Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer?
  • Mangoes trees
    Draw two sets of trees. The first tree has 2 branches and 8 mango fruits. The second tree has 3 branches and 12 mango fruits. Illustrate and express the ratio and proportion of the given statement.
  • Sandy
    Sandy, John and Marg baked pies for the Bake Sale. Sandy cut his pies into 6ths, John but his into 8ths, and Marg cut hers into quarters. Sandy sold 11/6, John sold  1 3/8 pies, and Marg sold 9/4 pies. Who sold the most pies? Who sold the fewest?
  • Pumpkin pie
    Have some pumpkin pie. One half of the pie is cut into 4 equal slices, the other half is cut into 3 equal slices. After eating one of the larger slices (on the 3 piece side), I wonder if I will eat more if I have one more from the 3 side, or two from the
  • Engineer Kažimír
    The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri
  • Simplest form of a fraction
    Which one of the following fraction after reducing in simplest form is not equal to 3/2? a) 15/20 b) 12/8 c) 27/18 d) 6/4
  • Ten fractions
    Write ten fractions between 1/3 and 2/3
  • Sort fractions
    Which is larger 3/7, 3/8, 3/9, 3/6 =
  • Math test
    Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.


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