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:

6 * 1/4 = 3/2 = 1 1/2 = 1.5

Spelled result in words is three halfs (or one and one half).

How do you solve fractions step by step?

  1. Multiple: 6 * 1/4 = 6 · 1/1 · 4 = 6/4 = 3 · 2/2 · 2 = 3/2
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 4) = 2. In the following intermediate step, cancel by a common factor of 2 gives 3/2.
    In other words - six multiplied by one quarter = three halfs.

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:

  • Zdeněk
    Zdeněk picked up 15 l of water from a 100-liter full-water barrel. Write a fraction of what part of Zdeněk's water he picked.
  • Fraction to decimal
    Write the fraction 3/22 as a decimal.
  • Babies
    There are 2 adults 2 children and 4 babies on a bus. What fraction of the people are babies?
  • In fractions
    An ant climbs 2/5 of the pole on the first hour and climbs 1/4 of the pole on the next hour. What part of the pole does the ant climb in two hours?
  • A quarter
    A quarter of the number 72 is:
  • Fruit basket
    If there are 7 apples and 5 oranges in the basket then what fraction of oranges are there in the fruit basket?
  • The correct
    The correct missing numerator in 2/4 = _/8 to make the fraction equal is
  • Evaluate expression
    Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2
  • Children 9
    There are 11 children in a room. 6 of the children are girls. What fraction of the children are girls?
  • One Saturday
    One Saturday evening there are 40 girls 25 boys 18 women and 17 men at a cinema. What fraction are girls?
  • Lowest terms 2
    The expression 4/12 can be expressed in its lowest term as 1/3. What is 3/15 expressed in its lowest term?
  • In the cafeteria
    There are 18 students in Jacob’s homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In simplest form, what fraction of students eat lunch in the cafeteria?
  • Someone
    Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake that is left, how much of a whole cake will you have eaten?


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