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 2/3) : (1/2) = 28/3 = 9 1/39.3333333

Spelled result in words is twenty-eight thirds (or nine and one third).

How do you solve fractions step by step?

  1. Conversion a mixed number 4 2/3 to a improper fraction: 4 2/3 = 4 2/3 = 4 · 3 + 2/3 = 12 + 2/3 = 14/3

    To find new numerator:
    a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3
    b) Add the answer from previous step 12 to the numerator 2. New numerator is 12 + 2 = 14
    c) Write a previous answer (new numerator 14) over the denominator 3.

    Four and two thirds is fourteen thirds
  2. Divide: 14/3 : 1/2 = 14/3 · 2/1 = 14 · 2/3 · 1 = 28/3
    Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/2 is 2/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - fourteen thirds divided by one half = twenty-eight thirds.

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:

  • Camp
    skauti In the camp are children. 1/2 went on a trip, 1/4 went to bathe, and 38 children remained in the room. How many children are in the camp?
  • Julian 2
    pizza Julian and two of his friends are going to share 1/4 of a pizza. How much will each person get?
  • Reciprocals
    reciprocal Which among the given reciprocal is correct a. 3/15x1/3= 1 b. 3/20x20/3=1 c. 7/14x7/7=1 d. 34/3x34/34=1
  • Almonds
    almonds Rudi has 4 cups of almonds. His trail mix recipe calls for 2/3 cup of almonds. How many batches of trail mix can he make?
  • Divide 11
    plusminus Divide the product of 4 and 5/8 by 1 1/2. Write your answer as a mixed number.
  • 6/24 change
    numbers 6/24 change to a fraction in lowest terms
  • Mrs. Zarka
    pie Mrs. Zarka has 3 pies for a party. She calculates that if she splits the pies evenly among the guests, they will each receive 1/6 of a pie. How many guests are there?
  • Chestnuts
    vaha Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of
  • Fruit punch
    juice Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5  liters of cranberry juice and 1 3/5  liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each
  • Leaking swimming pool
    bazen_kruh Between 10 P. M. and 7:10 A. M. , the water level in a swimming pool decreased by 5/12 inches . Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
  • Product of two fractions
    numbers Product of two fractions is 9 3/5 . If one of the fraction is 9 3/7. Find the other fraction.
  • Balls
    farebne-gulky The boys changed stamps, beads and balls. For 9 balls is 3 stamps, 2 balls is 44 stamps. How many beads is for 1 ball?
  • Fraction of a fraction
    plusminus What is two-quarters of twelve?


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