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:

6 4/12 - 5/10 = 35/6 = 5 5/6 ≅ 5.8333333

Spelled result in words is thirty-five sixths (or five and five sixths).

How do you solve fractions step by step?

  1. Conversion a mixed number 6 4/12 to a improper fraction: 6 4/12 = 6 4/12 = 6 · 12 + 4/12 = 72 + 4/12 = 76/12

    To find a new numerator:
    a) Multiply the whole number 6 by the denominator 12. Whole number 6 equally 6 * 12/12 = 72/12
    b) Add the answer from previous step 72 to the numerator 4. New numerator is 72 + 4 = 76
    c) Write a previous answer (new numerator 76) over the denominator 12.

    Six and four twelfths is seventy-six twelfths
  2. Subtract: 76/12 - 5/10 = 76 · 5/12 · 5 - 5 · 6/10 · 6 = 380/60 - 30/60 = 380 - 30/60 = 350/60 = 10 · 35/10 · 6 = 35/6
    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(12, 10) = 60. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 10 = 120. In the following intermediate step, cancel by a common factor of 10 gives 35/6.
    In other words - seventy-six twelfths minus five tenths = thirty-five sixths.

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:

  • A laundry
    Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
  • 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?
  • Regrouping
    Subtract mixed number with regrouping: 11 17/20- 6 19/20
  • Mountain
    Mountain has an elevation of 7450 meters and in the morning is the middle portion thereof in the clouds. How many meters of height is in the sky if below the clouds are 2,000 meters, and above clouds are two-fifths of the mountain's elevation?
  • Package
    The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
  • Claire and book
    After Claire has read the first 5/8 of the book, there are 120 pages left to read. What is the total number of pages of the book?
  • Two ribbons
    The total length of the two ribbons is 13 meters. If one ribbon is 7 and 5/8 meters long, what is the length of the other ribbon?
  • Coloured teacups
    The teacups in Tea Stop 55 are `2/5` green and `3/10` yellow. What fraction of the teacups are neither green nor yellow?
  • Erika admin
    Erika’s career consists of filing, typing and answering phones. She spends 1/6 of her time filing and 5/8 of her time typing. What fraction of her time does she spend answering phone calls?
  • Mike buys
    Mike buys flowers to plant around his trees. 3/8 of the flowers are red. 1/3 of the flowers are pink. The rest of the flowers are white. Find the fraction of flowers that are white.
  • Lunch time
    In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
  • Empty and full
    An empty can has a mass of 1/6 lb. When it is filled with sand, it has a mass of 7/12 lb. Find the mass of the sand in the can?
  • Mixed numbers
    Five and two-thirds minus 2 and one-half equals what number? A three and one-sixth B three and two-thirds C three and one-half D three and five-sixths


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