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:

2/3 * 3/4 = 1/2 = 0.5

Spelled result in words is one half.

How do you solve fractions step by step?

  1. Multiple: 2/3 * 3/4 = 2 · 3/3 · 4 = 6/12 = 1 · 6/2 · 6 = 1/2
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 12) = 6. In the following intermediate step, cancel by a common factor of 6 gives 1/2.
    In other words - two thirds multiplied by three quarters = one half.

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:

  • Watching TV
    tv2 One evening 2/3 of students watch TV. Of those students, 3/8 watched a reality show. Of the students that watched the show, 1/4 of them recorded it. What fraction of the students watched and recorded reality tv.
  • 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.
  • Farmers 2
    tomato On Wednesday the farmers at the Grant Farm picked 2 barrels of tomatoes. Thursday, the farmers picked 1/2 as many tomatoes as on Wednesday. How many barrels of tomatoes did the farmers pick on Thursday?
  • The tap
    kohutik For one day flows 148 l of water out of the tap. How much water will flow out for 3/4 day?
  • Coal mine
    coal The monthly plan of 17,000 tons of coal exceeded the mine by 1/25. How many tonnes of coal have been harvested from the mine above plan?
  • Algebra problem
    plusminus This is algebra. Let n represent an unknown number. 1. Eight more than the number n 2. Three times the number n 3. The product of the number n and eight 4. Three less than the number n 5. Three decreased by the number n
  • 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?
  • Toilets
    toilet Federal law requires that all residential toilets sold in the United States use no more than 1 3/5 gallons of water per flush. Before this legislation, conventional toilets used 3 2/5 gallons of water per flush. Find the amount of water saved in one year
  • Two thirds
    fractions Find two-thirds of the number equal to two-thirds of 99
  • Gear wheels
    gear Two gear wheels, which fit together, have the number of teeth z1=58 and z2=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute.
  • Camp
    skauti In the camp are children. 1/2 went on a trip, 1/4 went to bathe, and 38 children remained in the room. How many children are in the camp?
  • Youth track
    tunel Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate the size of subsidies to a trip group o
  • Drinking water
    blue-barrel A man drinks a keg of water in 40 days, and a woman drinks in 62 days. How many days do they consume a keg together?


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