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:

5/6 / 3/8 = 20/9 = 2 2/92.2222222

Spelled result in words is twenty ninths (or two and two ninths).

How do you solve fractions step by step?

  1. Divide: 5/6 : 3/8 = 5/6 · 8/3 = 5 · 8/6 · 3 = 40/18 = 2 · 20 /2 · 9 = 20/9
    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 3/8 is 8/3) 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 2 gives 20/9.
    In other words - five sixths divided by three eighths = twenty ninths.

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 quotient
    fractions What is the quotient of 3/10 divided by 2/4 as a fraction?
  • Divide 13
    delnik Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3
  • Pie division
    kolac 5/8 of a pie divide 6 pieces. Each friend got 1/6.  What fraction  of the whole pie does each person receive?
  • Fraction of a fraction
    plusminus What is two-quarters of twelve?
  • Lemonade 4
    lemonade Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
  • How many 16
    plusminus How many three-tenths are there in two and one-fourths?
  • Evaluate 12
    fractions Evaluate and simplify 9 divided by 7/6.
  • Percent calculation
    percent_sign Calculate 8% if 44% is 32.
  • Erik
    penize Three friends Peter, Erik and Milan shared 420 euros in a ratio of 1: 2: 3. How many euros did Erik get?
  • Monica 3
    clocks Monica works on her drawings for 2 hours. She spends 1/6 hour on each drawing. How many drawings does she work on in 2 hours?
  • Quotient and product
    plusminus If the quotient of [8/5 divided by 8/10] is added to the product of [8/14 x 7/12 x 3/8], what is the sum?
  • The physical
    clocks2 The physical therapist asks Mr. Smith to walk 20 minutes in one hour to improve his ambulation. What fractional part of an hour is Mr. Smith to exercise?
  • Day
    clock What part of the day are 23 hours 22 minutes? Express as a decimal number.


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