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:

2 * 1/3 = 2/3 ≅ 0.6666667

Spelled result in words is two thirds.

How do you solve fractions step by step?

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

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:

  • 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
  • A shopkeeper
    cheese A shopkeeper cuts a wheel of cheese into 10 equal wedges. A customer buys one-fifth of the wheel. How many wedges does the customer buy? Use the number line to help find the solution.
  • Jeffery
    painter Jeffery is painting a wall the width of the wall is 9 feet the length of the was is 8 2/3 feet what is the area of the wall Jeffery wants to paint?
  • Two xeroxes
    xerox The performances of the two copiers are in the ratio 3: 4. A machine with higher power will make 7,200 copies in one hour. How many copies will both machines make together in 5 hours?
  • The distance
    city The distance between two towns on a given map is 3 ½ cm. If ½ cm represents 6km. , what is the distance between the two towns?
  • Jewelry box
    ring The bottom of Zeyda's jewelry box is a rectangle with the length of 5 3/8 inches and a width of 3 1/4 inches. What is the area of the bottom of the jewelry box?
  • Multiplying fractions
    fractions What is 1/3 of 5?
  • Visit to grandfather
    family Shane's family traveled 3/10 of the distance to his grandfather’s house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his grandfather’s house was traveled on Sunday?
  • Quotient 3
    fractal If the quotient of 8/13 and 2 is subtracted from the product of 1 3/4 and 8/21, what is the difference?
  • Lengths of the pool
    bazen2 Miguel swam 6 lengths of the pool. Mat swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim?
  • 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?
  • The frame
    frame Rodney has a board that is 5/6 yards long. He cuts 1/5 yard off the board and uses the rest of the board to make a frame. How much of the board is used to make the frame?
  • Shirts
    blue shirts In a classroom,1/6 of the students are wearing blue shirts, and 2/3 are wearing white shirts. There are 18 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts?


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