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:

5 5/6 - 6 1/6 = -1/3 ≅ -0.3333333

Spelled result in words is minus one third.

How do you solve fractions step by step?

  1. Conversion a mixed number 5 5/6 to a improper fraction: 5 5/6 = 5 5/6 = 5 · 6 + 5/6 = 30 + 5/6 = 35/6

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6
    b) Add the answer from previous step 30 to the numerator 5. New numerator is 30 + 5 = 35
    c) Write a previous answer (new numerator 35) over the denominator 6.

    Five and five sixths is thirty-five sixths
  2. Conversion a mixed number 6 1/6 to a improper fraction: 6 1/6 = 6 1/6 = 6 · 6 + 1/6 = 36 + 1/6 = 37/6

    To find a new numerator:
    a) Multiply the whole number 6 by the denominator 6. Whole number 6 equally 6 * 6/6 = 36/6
    b) Add the answer from previous step 36 to the numerator 1. New numerator is 36 + 1 = 37
    c) Write a previous answer (new numerator 37) over the denominator 6.

    Six and one sixth is thirty-seven sixths
  3. Subtract: 35/6 - 37/6 = 35 - 37/6 = -2/6 = 2 · -1/2 · 3 = -1/3
    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(6, 6) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 6 = 36. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - thirty-five sixths minus thirty-seven sixths = minus one third.

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:

  • Mother 7
    Mother bought 18 fruits. 1/3 were pineapple and the rest  were mangoes . how many were mangoes
  • Kevin
    Kevin is baking brownies and needs peanuts.  The recipe calls for 1 and 2/3 cups of peanuts.  Kevin only has 5/6 of a cup of peanuts.  How many more cups of peanuts does Kevin need to have the correct amount?
  • When 5
    When 5 is subtracted from both my numerator and denominator I become 3/4. What fraction i am?
  • Equation with mixed 2
    A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X?
  • Mr. Peter
    Mr. Peter mowed 2/7 of his lawn. His son mowed 1/4 of it. Who mowed the most? How much of the lawn still need to be mowed?
  • 5 2/5
    5 2/5 hours a week  mathematics,  3 3/4 hours a week   Natural sciences, 4 3/8 hours a week  Technology . how many hours does  he spend on social sciences if he spend 17 1/2 hours a week for the four subject?
  • Karina
    Karina has 5 4/7 meters of cloth. She needs 3 1/6 meters of it in making a curtain for her window. How many meters of cloth were left to her after making the curtain?
  • There 14
    There are 250 people in a museum. 2/5 of the 250 people are girls 3/10 of the 250 people are boys The rest of the 250 people are adults Work out the number of adults in the museum.
  • Tree planting
    The trapezoidal garden has bases 44 m and 16 m long. Their distance is 25 m. How many square meters of its area will remain for tree planting if we use 1/5 of the entire site to construct a cottage, backyard, and road. Is it possible to determine the leng
  • Candies
    There are 150 candies in the bowl. Ivan took 7 thirtieths, Charles 6 fifteenths, and Thomas 3 tenths. How many sweets are left in the bowl?
  • Evaluate - lowest terms
    Evaluate: 16/25 - 11/25 (Express answer as a fraction reduced to lowest terms. )
  • Mixed numbers
    Five and two-thirds minus 2 and one-half equals what number? A three and one-sixth B three and two-thirds C three and one-half D three and five-sixths
  • Pizza fractions
    Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?


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