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 3/4 * 2 2/5 = 9/1 = 9

Spelled result in words is nine.

How do you solve fractions step by step?

  1. Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
    b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
    c) Write a previous answer (new numerator 15) over the denominator 4.

    Three and three quarters is fifteen quarters
  2. Conversion a mixed number 2 2/5 to a improper fraction: 2 2/5 = 2 2/5 = 2 · 5 + 2/5 = 10 + 2/5 = 12/5

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5
    b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
    c) Write a previous answer (new numerator 12) over the denominator 5.

    Two and two fifths is twelve fifths
  3. Multiple: 15/4 * 12/5 = 15 · 12/4 · 5 = 180/20 = 9 · 20/1 · 20 = 9
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the next intermediate step , cancel by a common factor of 20 gives 9/1.
    In words - fifteen quarters multiplied by twelve fifths = nine.

Rules for expressions with fractions:

Fractions - use the 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 non-zero 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:

  • Equivalent fractions
    equivalent-fractions Are these two fractions equivalent -4/9 and 11/15?
  • Fractions 3
    fractions_9 Calculate 1/9 of 27:
  • Compare
    fraction Compare fractions ?. Which fraction of the lower?
  • Write 3
    plusminus Write a real world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10 then solve the problem
  • Cake fractions
    dort Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
  • Two divided
    fractions14 Two divided by nine tenths.
  • Milimeters
    meter How many millimeters is 1/4 meters?
  • Pie
    pie_1 Vili ate three pieces of pie . If it piece is 1/8 how much pie did he eat?
  • Seeds
    klicenie Of the 72 wet seeds 7/8 germinated. How many seeds germinate?
  • Classroom 4
    skola_1 In a class of 36 pupils, 2/3 are girls. How much it is in a class girls and boys?
  • Women
    smajlik In an company of 1050 employees are 2/3 women. How many women work in the company?
  • Employees
    workers_45 Of all 360 employees, there are 11/12 women. How many men work in a company?
  • Mixed with percentages
    percent_21 Calculate 33 1/3% of 570.


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