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:

10 : (5/3) = 6/1 = 6

Spelled result in words is six.

How do you solve fractions step by step?

  1. Divide: 10 : 5/3 = 10/1 · 3/5 = 10 · 3/1 · 5 = 30/5 = 5 · 6 /5 · 1 = 6
    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 5/3 is 3/5) 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 5 gives 6/1.
    In other words - ten divided by five thirds = six.

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:

  • Cups
    We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then we
  • University bubble
    You'll notice that the college is up slowly every other high school. In Slovakia/Czech Republic, a lot of people are studying political science, mass media communication, social work, many sorts of management MBA. Calculate how many times more earns cleve
  • Day
    What part of the day are 23 hours 22 minutes? Express as a decimal number.
  • Camp
    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?
  • Gear wheels
    Two gear wheels, which fit together, have the number of teeth z1=58 and z2=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute.
  • Equation - inverse
    Solve for x: 7: x = 14: 1000
  • Julian 2
    Julian and two of his friends are going to share 1/4 of a pizza. How much will each person get?
  • One half 2
    One half pizza will be divide among 3 pupils. Each pupil receive 1/6. Is it true or false?
  • Pie division
    5/8 of a pie divide 6 pieces. Each friend got 1/6.  What fraction  of the whole pie does each person receive?
  • A landscaper
    A landscaper has 1/5 ton of dirt. She distributes it equally across three plots of land. What fraction of the dirt does each plot get?
  • Lauren
    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?
  • 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?
  • Lemonade 4
    Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?


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