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:

1/2 * 1/3 = 1/6 ≅ 0.1666667

Spelled result in words is one sixth.

How do you solve fractions step by step?

  1. Multiple: 1/2 * 1/3 = 1 · 1/2 · 3 = 1/6
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(1, 6) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - one half multiplied by one third = 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:

  • Fraction of a fraction
    plusminus What is two-quarters of twelve?
  • Berry Smoothie
    milk Rory has 5/8 cup of milk. How much milk does she have left after she doubles the recipe of the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanilla
  • Twelve eggs
    egg A dozen eggs cost 80 cents . how much will 3½ dozen eggs cost?
  • The number 4
    numbers Two-thirds of a number is negative six. Find the number.
  • In center
    number_line What number lies in the center between a quarter of a fifth and a half of a third on the number axis?
  • Lin has
    cake Lin has a cake pan that has a length of 8/3 inches, a width of 15/4 inches and a height of 3/2 inches. What is the volume of the cake pan?
  • Eight pipes
    pipe1 Eight pipes are each 2¼m long . what is the total length of the eight pipes?
  • Percent calculation
    percent_sign Calculate 8% if 44% is 32.
  • Fractions mul add sum
    fractions To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Dice and coin
    dice A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
  • Tablespoon of salt
    vaha Mrs. Monika uses 3/4 tablespoons of salt for every kilogram of ground pork. How many tablespoons of salt will she use for 3 1/2 kilograms of ground pork?
  • The elevation
    ship The elevation of a sunken ship is -120 feet. Your elevation is 5/8 of the ship’s elevation. What is your elevation?
  • There 11
    venn There are 50 pupil in the class. Out of of this number,1/10 speak French only and 4/5 of the 10 remainder speak both French and English . If the rest speak English only find the number of students who speak only English?


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