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 1/2 + 1 1/3 = 23/6 = 3 5/63.8333333

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

How do you solve fractions step by step?

  1. Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2
    b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
    c) Write a previous answer (new numerator 5) over the denominator 2.

    Two and one half is five halfs
  2. Conversion a mixed number 1 1/3 to a improper fraction: 1 1/3 = 1 1/3 = 1 · 3 + 1/3 = 3 + 1/3 = 4/3

    To find new numerator:
    a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3
    b) Add the answer from previous step 3 to the numerator 1. New numerator is 3 + 1 = 4
    c) Write a previous answer (new numerator 4) over the denominator 3.

    One and one third is four thirds
  3. Add: 5/2 + 4/3 = 5 · 3/2 · 3 + 4 · 2/3 · 2 = 15/6 + 8/6 = 15 + 8/6 = 23/6
    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(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - five halfs plus four thirds = twenty-three sixths.

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:

  • Sum of fractions
    fractions What is the sum of 2/3+3/5?
  • Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356
  • Berry Smoothie
    milk Rory has 5/8 cup of milk. How much milk does she have left after she doubles the recipe of the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanilla
  • Rose spends
    clocks2 Rose spends 2 1/3 hours studying Math, 1 3/4 hours studying English, and 2 1/4 hours studying Science. Find her average time studying the three subjects.
  • 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?
  • Ingrid
    tv Ingrid watched television for 2 1/4 hours, and Devon watched for 3 2/3 hours. For how many hours did they watch television in total?
  • A man 3
    pears A man buys a box of fruits containing 286 fruits out of these 1/2 are apples and the rest are pears. 4/13 of the pears are rotten. He sells the good pears at rupees 4 1/11 each. How much money does he receive on selling the good pears?
  • Stock
    frac Enterprise sold 7/12 of their products to foreign markets and 2/5 of the remainder sold at home. How many % of the products is still in stock?
  • Savings
    savings Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
  • Sum three fractions
    plusminus Work out the sum of 1/4, 1/5 and 3/10.
  • Addition of mixed numerals
    scientific Add two mixed fractions: 2 4/6 + 1 3/6
  • Salad
    salát We need two tenths kg of a carrot, one tenth of peas and three tenths of of tomatoes to make salad. Express the fraction of the weight of the vegetables to be salad. Convert the result to grams.
  • Bus vs train
    Clock0400 Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out?


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