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:

3/5 + 1/6 = 23/300.7666667

Spelled result in words is twenty-three thirtieths.

How do you solve fractions step by step?

  1. Add: 3/5 + 1/6 = 3 · 6/5 · 6 + 1 · 5/6 · 5 = 18/30 + 5/30 = 18 + 5/30 = 23/30
    For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 6) = 30. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 6 = 30. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - three fifths plus one sixth = twenty-three thirtieths.

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:

  • Adding mixed 4
    2 and 1/8th plus 1 and 1/3rd =
  • Pizza fractions
    Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • Peter 2
    Peter wanted to have 120 kilogram of fruits.  He picked 10 bags .  each bags contains 9 1/2 kilograms. How many kilograms he need more?
  • Birthday party
    For her youngest son's birthday party, the mother bought 6 3/4 kg of hotdog and 5 1/3 dozens bread rolls. Hotdogs cost 160 per kilogram, and a dozen bread rolls cost 25. How much did she spend in all?
  • Three rectangles
    Some wire is used to make 3 rectangles: A, B, and C. Rectangle B's dimensions are 3/5 cm larger than Rectangle A's dimensions, and Rectangle C's dimensions are again 3/5 cm larger than Rectangle B's dimensions. Rectangle A is 2 cm by 3 1/5 cm. What is the
  • Infinite sum of areas
    Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tr
  • Lengths of the pool
    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?
  • Rachel
    Rachel fills 9/10 of a bucket with water and 3/5 of another bucket at the same size. How muck water does she have in total?
  • Two numbers 11
    The sum of two rational numbers is (-2). If one of them is 3/5, find the other.
  • What is 13
    What is the number sentence? * 1 point 1/2 + 3/4 + 1/4 = A 1/2 - 3/4 - 1/4 = B 1/2 x 3/4 x 1/4 = C 1/2 ÷ 3/4 ÷ 1/4 = D
  • Farmer 5
    Farmer Joe ordered 3 bags of soil last month. Each bag weighed 4 ⅖ kilograms. He used the first bag in a week. At the end of this month, there were 2 ¾ kilograms of soil left in the second bag and ⅞ kilograms of soil left in the third bag. How much soil w
  • Fruit basket 2
    The weight of the empty fruit basket is ¾ kg. We added ½ kg apples and 5/4 kg guavas. What will be the total weight of the fruit basket?
  • Evaluate 17
    Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.


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