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:

3/5÷3 = 1/5 = 0.2

Spelled result in words is one fifth.

How do you solve fractions step by step?

  1. Divide: 3/5 : 3 = 3/5 · 1/3 = 3 · 1/5 · 3 = 3/15 = 3 · 1 /3 · 5 = 1/5
    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 3/1 is 1/3) 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 3 gives 1/5.
    In other words - three fifths divided by three = one fifth.

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:

  • Unknown number
    I think the number - its sixth is 3 smaller than its third.
  • Reciprocal equation 3
    Solve reciprocal equation: 1/2 + 2/3=1/x
  • Chocolate
    Children break chocolate first to third and then every part of another half. What kind got each child? Draw a picture. What part would have received if each piece have halved?
  • Sewing
    The lady cut off one-half of the cloth. She needed three-quarters of this piece to sew a skirt. What part of the original piece of cloth remained?
  • Tank 11
    When 150 litres has been drawn from a tank it is 3/8 full, how many litres will the tank hold?
  • Dividends
    The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
  • The buns
    Kate, Zofia, and Peter Liked buns. Even today, their grandmother prepares their favorite meal. Katka eats 4 bunches, Žofia 3, and Petra eats 5 buns. Their grandmother said to them, "My inmate will you know how many buns I have been made today if those you
  • 3 children
    3 children had to divide 4 pounds is candy. How much candy did each child get?
  • UN 1
    If we add to an unknown number his quarter, we get 210. Identify unknown number.
  • Equation
    Solve equation and check the result: 1.4x - 3/2 + x - 9,8 = x + 0,4/3 - 7 + 1,6/6
  • Summerjob
    Miloš saved a quarter of the money from the summerjob, bought a winter jacket for half, bought gifts for his parents and siblings for a sixth, and still had CZK 400 left. How much did Miloš earn?
  • Honza
    Honza is 13 years old and Peter 21 years old. After how many years are their ages will be at ratio 7: 9?
  • Class 8.A
    Three quarters of class 8.A went skiing. Of those who remained at home one third was ill and the remaining six were on math olympic. How many students have class 8.A?


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