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:

- 3/8 * -4/9 = 1/6 ≅ 0.1666667

Spelled result in words is one sixth.

How do you solve fractions step by step?

  1. Unary minus: -3/8 = -3/8
  2. Multiple: the result of step No. 1 * (-4) = -3/8 * (-4) = -3 · (-4)/8 · 1 = 12/8 = 3 · 4/2 · 4 = 3/2
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 8) = 4. In the next intermediate step, , cancel by a common factor of 4 gives 3/2.
    In words - minus three eighths multiplied by minus four = three halfs.
  3. Divide: the result of step No. 2 : 9 = 3/2 : 9 = 3/2 · 1/9 = 3 · 1/2 · 9 = 3/18 = 3 · 1 /3 · 6 = 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 9/1 is 1/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 3 gives 1/6.
    In words - three halfs divided by nine = one sixth.

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:

  • Length subtracting
    meter_11 Express in mm: 5 3/10 cm - 2/5 mm
  • Add sub fractions
    fractions_2 What is 4 1/2+2/7-213/14?
  • School
    skola_16 There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males?
  • Fractions mul add sum
    fractions_3 To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Pizza fractions
    pizza Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • 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?
  • Difference mixed fractions
    mixed_fractions_1 What is the difference between 4 2/3 and 3 1/6?
  • Mixed numbers
    zlomky_10 Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3
  • Pounds
    jablka_8 3 pounds subtract 1/3 of a pound.
  • Michael
    chocholate Michael had a bar if chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
  • Find the 24
    plusminus_1 Find the difference between 2/7 and 1/21
  • From a
    meter_2 From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece?
  • King
    kral King had four sons. First inherit 1/2, second 1/4 , third 1/5 of property. What part of the property was left to the last of the brothers?


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