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 3/4 * 2 2/5 = 9/1 = 9

Spelled result in words is nine.

How do you solve fractions step by step?

  1. Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
    b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
    c) Write a previous answer (new numerator 15) over the denominator 4.

    Three and three quarters is fifteen quarters
  2. Conversion a mixed number 2 2/5 to a improper fraction: 2 2/5 = 2 2/5 = 2 · 5 + 2/5 = 10 + 2/5 = 12/5

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5
    b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
    c) Write a previous answer (new numerator 12) over the denominator 5.

    Two and two fifths is twelve fifths
  3. Multiple: 15/4 * 12/5 = 15 · 12/4 · 5 = 180/20 = 9 · 20/1 · 20 = 9
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the next intermediate step, , cancel by a common factor of 20 gives 9/1.
    In words - fifteen quarters multiplied by twelve fifths = nine.

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:

  • Paper clips
    paper Mrs. Bright is organizing her office supplies. There are 5 open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left?
  • A shopkeeper
    cheese A shopkeeper cuts a wheel of cheese into 10 equal wedges. A customer buys one-fifth of the wheel. How many wedges does the customer buy? Use the number line to help find the solution.
  • Tallest and shortest
    meter Jenn is the tallest on the team. He is 1 1/2 times as tall as the shortest girl whom is 4 1/4 feet tall. How tall is Jebb?
  • Lenth - meter
    meter Find in centimeters, 3/10 of half meter.
  • Fitness center
    time Every Wednesday, Monica works out for 3/4  of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?
  • 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
  • Hotel 4
    manderlak A 360 room hotel has 1/3 of its rooms occupied at present . How many rooms are empty?
  • Boats 2
    ship Three quarters of the boats in the marina are white 4/7 of the remaining boats are blue, rest are red if there are 9 red boats. How many boats are in the marina?
  • Shirts
    skola In a classroom, 1/6 of the students are wearing blue shirts and 2/3 are wearing white shirts. There are 36 students in the class. How many students are wearing a shirt other than blue or white?
  • The difference 2
    numbs The difference between the two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number?
  • Pumps
    fuel_tank 6 pump fills the tank for 3 and a half days. How long will fill the tank 7 equally powerful pumps?
  • 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
  • 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?


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