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 2/3 + 3 1/12 = 23/4 = 5 3/4 = 5.75

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

How do you solve fractions step by step?

  1. Conversion a mixed number 2 2/3 to a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
    b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
    c) Write a previous answer (new numerator 8) over the denominator 3.

    Two and two thirds is eight thirds
  2. Conversion a mixed number 3 1/12 to a improper fraction: 3 1/12 = 3 1/12 = 3 · 12 + 1/12 = 36 + 1/12 = 37/12

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/12 = 36/12
    b) Add the answer from previous step 36 to the numerator 1. New numerator is 36 + 1 = 37
    c) Write a previous answer (new numerator 37) over the denominator 12.

    Three and one twelfth is thirty-seven twelfths
  3. Add: 8/3 + 37/12 = 8 · 4/3 · 4 + 37/12 = 32/12 + 37/12 = 32 + 37/12 = 69/12 = 3 · 23/3 · 4 = 23/4
    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(3, 12) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 12 = 36. In the next intermediate step, , cancel by a common factor of 3 gives 23/4.
    In words - eight thirds plus thirty-seven twelfths = twenty-three quarters.

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:

  • Expressions
    plusminus 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
  • Math homework
    clocks2 It took Jose two-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, any two- fifths of an hour on Wednesday. How many hours did it take Jose to complete his homework altogether?
  • Evaluate
    calculator The division of numbers 6 and 3 increase by-product of the numbers 115 and 0.1
  • A shopkeeper 3
    apples A shopkeeper sells 8 1/3 kg, 10 1/4 kg and 11 1/5 kg of apples on 3 consecutive days. What is the total weight of apples sold?
  • Bathroom 4
    water Dolor puts 3 1/2 pails of water into a water container in the bathroom every day. Her daughter, Lei, uses 2 1/4 pails of water every day when taking a bath. If the water container had 5 5/8 pails of water at the start, how much water is left in it after 5
  • The Mayflower
    storm-012 The Mayflower traveled for 66 days on the trip from England to America. The weather was storming for many days of their trip. If one and a half of the days at Sea where Sunny with good weather, 1/6 of the days were sunny but very windy and the other days
  • 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
  • Pizza fractions
    pizza Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • Two pizzas
    pizza Jacobs mom bought two whole pizzas. He ate 2/10 of the pizza and his dad ate 1 1/5. How much is left.
  • A large 2
    cinema2 A large popcorn bag holds four times as much as a small popcorn bag at the end of the party 3 1/3 small bags and 2 1/4 large bags left. How many small bags with the leftover popcorn fill?
  • Walk for exercise
    runners Anya, Jose, Cali, and Stephan walk for exercise. Anya's route is 2 1/4 kilometers long. Jose's route is 1 1/2 fewer km. Cali's route is 1 1/2  times as long as Jose's route, and 2 fewer km than Stephan's route. What distance (S) is Stephan's route?
  • Diophantus
    diofantos We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth las
  • Food weight
    vaha Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 o


next math problems »