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 2/3 - 5 5/9 = -17/9 = -1 8/9 ≅ -1.8888889

Spelled result in words is minus seventeen ninths (or minus one and eight ninths).

How do you solve fractions step by step?

  1. Conversion a mixed number 3 2/3 to a improper fraction: 3 2/3 = 3 2/3 = 3 · 3 + 2/3 = 9 + 2/3 = 11/3

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 3. Whole number 3 equally 3 * 3/3 = 9/3
    b) Add the answer from previous step 9 to the numerator 2. New numerator is 9 + 2 = 11
    c) Write a previous answer (new numerator 11) over the denominator 3.

    Three and two thirds is eleven thirds
  2. Conversion a mixed number 5 5/9 to a improper fraction: 5 5/9 = 5 5/9 = 5 · 9 + 5/9 = 45 + 5/9 = 50/9

    To find new numerator:
    a) Multiply the whole number 5 by the denominator 9. Whole number 5 equally 5 * 9/9 = 45/9
    b) Add the answer from previous step 45 to the numerator 5. New numerator is 45 + 5 = 50
    c) Write a previous answer (new numerator 50) over the denominator 9.

    Five and five ninths is fifty ninths
  3. Subtract: 11/3 - 50/9 = 11 · 3/3 · 3 - 50/9 = 33/9 - 50/9 = 33 - 50/9 = -17/9
    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(3, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 9 = 27. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - eleven thirds minus fifty ninths = minus seventeen ninths.

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:

  • Bucket 4
    kanister The bucket has 5/8 gallons of water. The bucket tips over, and 7/12 gallon of water pours out. How much water is left in the bucket, in gallons, written as a fraction?
  • 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.
  • Mrs. Susan
    textiles Mrs. Susan bought 1/8 m of curtain cloth. She used 3/5 m to make a curtain for the living room window. How many meters of cloth were not used?
  • Regrouping
    mixed Subtract mixed number with regrouping: 11 17/20- 6 19/20
  • Players - baseball
    balls2 There are 20 players on each of two baseball teams. If 2/5 of the players on team 1 miss practice and 1/4 of the players on team two miss practice, how many more players from team 1 missed practice then team 2?
  • Plums
    plumbs In the bag was to total 136 plums. Igor took 3 plums and Mary took 4/7 from the rest. How many plums remained in the bag?
  • 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?
  • Pediatrician
    doctor Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work?
  • Equation with mixed 2
    mixed A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X?
  • Cookies
    cookies In a cookie jar, 1/4 of the cookies are chocolate chip and 1/2 of the rest are peanut butter. What fraction of all the cookies are peanut butter?
  • Sugar 8
    sugar Heather has 2 cups of powdered sugar. She sprinkles 3/5 of the sugar onto a plate of brownies and sprinkles the rest into a plate of lemon cookies. How much sugar does Heather sprinkle on the brownies? How much sugar does Heather sprinkle on the lemon coo
  • Interior designer
    draperies To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?
  • You leave
    meter You leave school and the end of the day and walk 3/8 of a mile away before realizing that you left your backpack and immediately turn around you then walk 1/6 of a mile back towards school at this point assuming you walked in a straight line how many mile


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