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 1/3 + 2 1/3 = 11/3 = 3 2/3 ≅ 3.6666667

Spelled result in words is eleven thirds (or three and two thirds).

How do you solve fractions step by step?

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

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3
    b) Add the answer from previous step 3 to the numerator 1. New numerator is 3 + 1 = 4
    c) Write a previous answer (new numerator 4) over the denominator 3.

    One and one third is four thirds
  2. 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
  3. Add: 4/3 + 7/3 = 4 + 7/3 = 11/3
    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(3, 3) = 3. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 3 = 9. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - four thirds plus seven thirds = eleven 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:

  • The book 4
    books Mr. Kinion read 3 3/4 chapters in his book on Monday. He then read 2 4/6 more chapters on Tuesday. How many chapters has he read so far?
  • Savings
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  • Patel
    juice Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, StartFraction 9 over 20 E
  • The pet
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  • Flower garden
    flowers2 In the mr elliots garden 1/8 of the flowers are red 1/4 of them are purple and 1/4 of the remaning flowers are pink. If there is 128 flowers how many of them are pink?
  • Two numbers
    third The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
  • Weigh in total
    hrozno I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total?
  • Product and sum
    fractions14 What is the product of two fourths  and the sum of three halves and four?
  • Evaluate 17
    fractions Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.
  • Pupils
    school Two classes want to collect money. Boys are four-seventh pupils. In time did not pay a quarter of the boys and a sixth of girls, which mean 12 sinners. How many pupils attend these two classes?
  • Stones in aquarium
    akvarko In an aquarium with a length of 2 m, 1.5 m wide, and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
  • Diophantus
    diofantos We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth las
  • Adding
    eq1 Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.


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