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 2/5 / 1 1/5 = 11/3 = 3 2/33.6666667

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 4 2/5 to a improper fraction: 4 2/5 = 4 2/5 = 4 · 5 + 2/5 = 20 + 2/5 = 22/5

    To find a new numerator:
    a) Multiply the whole number 4 by the denominator 5. Whole number 4 equally 4 * 5/5 = 20/5
    b) Add the answer from previous step 20 to the numerator 2. New numerator is 20 + 2 = 22
    c) Write a previous answer (new numerator 22) over the denominator 5.

    Four and two fifths is twenty-two fifths
  2. Conversion a mixed number 1 1/5 to a improper fraction: 1 1/5 = 1 1/5 = 1 · 5 + 1/5 = 5 + 1/5 = 6/5

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
    b) Add the answer from previous step 5 to the numerator 1. New numerator is 5 + 1 = 6
    c) Write a previous answer (new numerator 6) over the denominator 5.

    One and one fifth is six fifths
  3. Divide: 22/5 : 6/5 = 22/5 · 5/6 = 22 · 5/5 · 6 = 110/30 = 10 · 11 /10 · 3 = 11/3
    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 6/5 is 5/6) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 10 gives 11/3.
    In other words - twenty-two fifths divided by six fifths = eleven thirds.

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 baker
    pie A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie. How many pieces of pie does she have?
  • Cooks
    kucharky Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes?
  • Barbara 2
    pizza Barbara get 6 pizzas to divide equally among 4 people. How much of a pizza can each person have?
  • Fraction expression
    fractions Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
  • Lauren
    clocks Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each student, one at a time, for three-fourths of an hour, how many students does she tutor?
  • Division by zero
    infinity-512 Fraction 5 by 2. if 3 is added to numerator and 2 is subtracted from the denominator then the new fraction is:
  • The Hobson
    fuel The Hobson family is on a road trip and their gas tank is 1/10 full. If they can drive 40 more miles, what fraction of the tank does each mile consume?
  • Francesca
    meter Francesca is growing 1/2 inch each year. How many years will it take for her to grow 6 inches?
  • What is 13
    plusminus What is the number sentence? * 1 point 1/2 + 3/4 + 1/4 = A 1/2 - 3/4 - 1/4 = B 1/2 x 3/4 x 1/4 = C 1/2 ÷ 3/4 ÷ 1/4 = D
  • Pizza 5
    pizza You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get?
  • 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?
  • Cake 7
    cake 1/3 of a cake shared with 4 people. What share of the whole cake has each people?
  • Brooke
    plusminus Brooke divided 2/3 by 1/6 and got 1/9. Her classmate told her that she isn’t correct. What do you think went wrong with Brooke’s solution? Explain your answer in 2 - 3 sentences.


next math problems »