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 1/2 - 2 1/4 = 5/4 = 1 1/4 = 1.25

Spelled result in words is five quarters (or one and one quarter).

How do you solve fractions step by step?

  1. Conversion a mixed number 3 1/2 to a improper fraction: 3 1/2 = 3 1/2 = 3 · 2 + 1/2 = 6 + 1/2 = 7/2

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2
    b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
    c) Write a previous answer (new numerator 7) over the denominator 2.

    Three and one half is seven halfs
  2. Conversion a mixed number 2 1/4 to a improper fraction: 2 1/4 = 2 1/4 = 2 · 4 + 1/4 = 8 + 1/4 = 9/4

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4
    b) Add the answer from previous step 8 to the numerator 1. New numerator is 8 + 1 = 9
    c) Write a previous answer (new numerator 9) over the denominator 4.

    Two and one quarter is nine quarters
  3. Subtract: 7/2 - 9/4 = 7 · 2/2 · 2 - 9/4 = 14/4 - 9/4 = 14 - 9/4 = 5/4
    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(2, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - seven halfs minus nine quarters = five 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:

  • Math test
    test Obelix filled a mathematical test in which he answered 25 questions. For every correct answer, he received 5 points, for each bad answer he had 3 points deducted. Obelix gained 36% of all points in the test. How many questions did he solve correctly?
  • Package
    latky The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
  • Sadie
    books Sadie practiced her spelling words for 3/4 of an hour, and Max practiced his spelling words for 5/12 of an hour. In the simplest form, how much longer did Sadie practice than Max?
  • Cups of flour
    vahy2 Jade was baking cupcakes for her class. She has 4 5/4 cups of flour.  For one batch, she used 1 2/3 cups of flour.  On another batch, she used 7/9 of a cup of flour.  How much flour does Jade have left after making the two batches of cupcakes?
  • Find the 24
    plusminus Find the difference between 2/7 and 1/21
  • Issac
    pizza Issac eats 1/6 of the pizza. Maya then eats 3/5 of the remaining pizza. What fraction of the original pizza is left?
  • Ali bought
    milk Ali bought 5/6 litre of milk. He drank 1/2 litre and his brother drank 1/6 litre. How much litre of milk left?
  • Pounds
    jablka 3 pounds subtract 1/3 of a pound.
  • 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?
  • Rita has
    meter Rita has 3/4 m of ifugao cloth. She used 2/3 m for placement. What part of ifugao cloth was left?
  • A 14.5-gallon
    fuel A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number.
  • Cereals
    kombajn Ari and Joey share a 30-ounce box of cereal. By the end of the week, Ari has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box?
  • The frame
    frame Rodney has a board that is 5/6 yards long. He cuts 1/5 yard off the board and uses the rest of the board to make a frame. How much of the board is used to make the frame?


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