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 = 2/30.6666667

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 following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - two multiplied by one third = two thirds.

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:

  • Ms. Sheppard
    flowers2 Ms. Sheppard cuts ½ of a piece of construction paper. She uses ⅙ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?
  • Slices of pizza
    pizza Maria ate 1/4 of a pizza. If there were 20 slices of pizza, how many slices did Maria eat?
  • The ketchup
    tomato If 3 1/4 of tomatoes are needed to make 1 bottle of ketchup. Find the number of tomatoes required to make 4 1/5 bottles
  • Tallest and shortest
    meter Jenn is the tallest on the team. He is 1 1/2 times as tall as the shortest girl whom is 4 1/4 feet tall. How tall is Jebb?
  • Mountain
    manga_parbat Mountain has an elevation of 7450 meters and in the morning is the middle portion thereof in the clouds. How many meters of height is in the sky if below the clouds are 2,000 meters, and above clouds are two-fifths of the mountain's elevation?
  • Lenth - meter
    meter Find in centimeters, 3/10 of half meter.
  • Water in body
    Water-in-human-body Water in the human organism of all the compounds represented constitutes about 3/5 of the total weight. How many kilograms of water is in your body when you weigh 51 kg?
  • Each year
    zosity Each year, Mr. Baumann purchases enough paper for his 16 students. If each student will use 3/4 pack of paper, how many packs of paper will he need to purchase? Answer as a mixed number or as a whole number.
  • Length 7
    square_numbers Length equals 7/6 inch in width equals 7/9 inches the area is?
  • Boys and girls
    skola If the ratio of male & female teachers is 2/5 & it is in proportion of the male & female students, how many are girls if there are 42 boys?
  • Magic bag
    mince Each time the prince crossed the bridge, the number of tolars in the magic bag doubled. But then the devil always conjured 300 tolars for him. When this happened for the third time, the prince had twice as much as he had in the beginning. How many tolars
  • The ratio 4
    ratios2 The ratio of two number is 5:4 if 40% of the first number is 12, what will be 50% of the second number?
  • Pumps
    fuel_tank 6 pump fills the tank for 3 and a half days. How long will fill the tank 7 equally powerful pumps?


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