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 4/18 + 6/18 = 23/9 = 2 5/92.5555556

Spelled result in words is twenty-three ninths (or two and five ninths).

How do you solve fractions step by step?

  1. Conversion a mixed number 2 4/18 to a improper fraction: 2 4/18 = 2 4/18 = 2 · 18 + 4/18 = 36 + 4/18 = 40/18

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 18. Whole number 2 equally 2 * 18/18 = 36/18
    b) Add the answer from previous step 36 to the numerator 4. New numerator is 36 + 4 = 40
    c) Write a previous answer (new numerator 40) over the denominator 18.

    Two and four eighteenths is forty eighteenths
  2. Add: 40/18 + 6/18 = 40 + 6/18 = 46/18 = 2 · 23/2 · 9 = 23/9
    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(18, 18) = 18. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 18 × 18 = 324. In the following intermediate step, cancel by a common factor of 2 gives 23/9.
    In other words - forty eighteenths plus six eighteenths = twenty-three ninths.

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:

  • Expressions
    Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n
  • Fe metal sheet
    For one product, 5/8 of the metal sheet are consumed, to the second 5/6 of remains. What part of the sheet metal is consumed for both products together?
  • Simplify 3
    Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  • Add two fractions
    What is the sum of 2/3 and 3/10?
  • Adding mixed fractions
    Add this two mixed numbers: 1 5/6 + 2 2/11=
  • One evening
    One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all?
  • A market
    A market vendor was able to sell all the mangoes, papayas, and star apples.  1/5  of the fruits were mangoes,   2/3  of them were papayas and the rest were star apples.  How many parts of the fruits sold are star apples?
  • Adding mixed numbers
    Add this two mixed numbers: 1 5/6 + 2 2/11=
  • An orchard
    During a visit to an orchard, Greg picked 3/5 of a bag of delicious golden apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in t
  • Circular garden
    Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante
  • Adding mixed 4
    2 and 1/8th plus 1 and 1/3rd =
  • Roses and tulips
    At the florist are 50 tulips and 5 times fewer roses. How many flowers are in the flower shop?
  • Honey 3
    Honey jogged 1 3/4 km on Monday,1 1/2 km on Wednesday and 1  2/3 km on Friday . how far did he jog?


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