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:

8 4/6 - 5 8/12 = 3/1 = 3

Spelled result in words is three.

How do you solve fractions step by step?

  1. Conversion a mixed number 8 4/6 to a improper fraction: 8 4/6 = 8 4/6 = 8 · 6 + 4/6 = 48 + 4/6 = 52/6

    To find a new numerator:
    a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6
    b) Add the answer from previous step 48 to the numerator 4. New numerator is 48 + 4 = 52
    c) Write a previous answer (new numerator 52) over the denominator 6.

    Eight and four sixths is fifty-two sixths
  2. Conversion a mixed number 5 8/12 to a improper fraction: 5 8/12 = 5 8/12 = 5 · 12 + 8/12 = 60 + 8/12 = 68/12

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 12. Whole number 5 equally 5 * 12/12 = 60/12
    b) Add the answer from previous step 60 to the numerator 8. New numerator is 60 + 8 = 68
    c) Write a previous answer (new numerator 68) over the denominator 12.

    Five and eight twelfths is sixty-eight twelfths
  3. Subtract: 52/6 - 68/12 = 52 · 2/6 · 2 - 68/12 = 104/12 - 68/12 = 104 - 68/12 = 36/12 = 12 · 3/12 · 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, 12) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 12 = 72. In the following intermediate step, cancel by a common factor of 12 gives 3/1.
    In other words - fifty-two sixths minus sixty-eight twelfths = three.

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:

  • A market
    A market vendor was able to sell all the mangoes, papayas, and star apples.  1/5  of the fruits were mangoes,   2/3  of them were papayas and the rest were star apples.  How many parts of the fruits sold are star apples?
  • Difference of two fractions
    What is the difference between 1/2 and 1/6? (Write the answer as a fraction in lowest terms. )
  • Pounds
    Three pounds subtract 1/3 of a pound.
  • Pupils 7
    There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls?
  • Emily
    Emily had 20 minutes to do a three-problem quiz. She spent 11 3/4 minutes on question A and 5 1/2 minutes on question B. How much time did she have left for question C?
  • Plums
    In the bag was to total 136 plums. Igor took 3 plums and Mary took 4/7 from the rest. How many plums remained in the bag?
  • The pet
    Ananya has a bunny. She bought 4 7/8 pounds of carrots. She fed her bunny 1 1/4 pounds of carrots the first week. She fed her bunny 5/6 pounds of carrots the second week. All together, how many pounds of carrots did she feed her bunny? 1. Draw a tape diag
  • A 14.5-gallon
    A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number.
  • Evaluate 17
    Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.
  • Pizzas
    Billy ate 1 1/4 pizzas and John ate 1 2/3 pizzas. How much more pizza did John eat than Billy?
  • Magic bag
    Each time the prince crossed the bridge, the number of tolars in the magic bag doubled. But then the devil always conjured 300 tolars for him. When this happened for the third time, the prince had twice as much as he had in the beginning. How many tolars
  • Seven up
    Peter barman is making 8 gallons of Tropical trip punch. He has already poured in 1 3/4 gal of pineapple juice and 2 1/2 gal of orange juice. The only other ingredient us 7-Up. How much does 7-Up does Peter need?
  • Players - baseball
    There are 20 players on each of two baseball teams. If 2/5 of the players on team 1 miss practice and 1/4 of the players on team two miss practice, how many more players from team 1 missed practice then team 2?


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