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:

14 5/10 - 12 9/10 = 8/5 = 1 3/5 = 1.6

Spelled result in words is eight fifths (or one and three fifths).

How do you solve fractions step by step?

  1. Conversion a mixed number 14 5/10 to a improper fraction: 14 5/10 = 14 5/10 = 14 · 10 + 5/10 = 140 + 5/10 = 145/10

    To find a new numerator:
    a) Multiply the whole number 14 by the denominator 10. Whole number 14 equally 14 * 10/10 = 140/10
    b) Add the answer from previous step 140 to the numerator 5. New numerator is 140 + 5 = 145
    c) Write a previous answer (new numerator 145) over the denominator 10.

    Fourteen and five tenths is one hundred forty-five tenths
  2. Conversion a mixed number 12 9/10 to a improper fraction: 12 9/10 = 12 9/10 = 12 · 10 + 9/10 = 120 + 9/10 = 129/10

    To find a new numerator:
    a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10/10 = 120/10
    b) Add the answer from previous step 120 to the numerator 9. New numerator is 120 + 9 = 129
    c) Write a previous answer (new numerator 129) over the denominator 10.

    Twelve and nine tenths is one hundred twenty-nine tenths
  3. Subtract: 145/10 - 129/10 = 145 - 129/10 = 16/10 = 2 · 8/2 · 5 = 8/5
    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(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 8/5.
    In other words - one hundred forty-five tenths minus one hundred twenty-nine tenths = eight fifths.

Rules for expressions with fractions:

Fractions - simply use a forward 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 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:

  • Difference between fractions
    What is the difference when you take away 1/6 from 2/8?
  • Sadie
    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?
  • Bitoo and Reena
    Bitoo ate 3/5 part of an apple and the remaining part was eaten by his sister Reena. How much part of an apple did Renna eat? Who had the larger share? By how much?
  • Find the 24
    Find the difference between 2/7 and 1/21
  • Cups of flour
    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?
  • From a 2
    From a rope that is 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope?
  • Rita has
    Rita has 3/4 m of Ifugao cloth. She used 2/3 m for placement. What part of Ifugao cloth was left?
  • A basket 2
    A basket contains three types of fruits weighing 87/4 kg in all. If 23/4 kilograms of these are oranges, 48/7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket?
  • Cereals
    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?
  • A 14.5-gallon
    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.
  • Fractions mul add sum
    To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Cake fractions
    Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
  • The 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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