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:

8 2/3 - 3 5/7 = 104/21 = 4 20/214.952381

Spelled result in words is one hundred four twenty-firsts (or four and twenty twenty-firsts).

How do you solve fractions step by step?

  1. Conversion a mixed number 8 2/3 to a improper fraction: 8 2/3 = 8 2/3 = 8 · 3 + 2/3 = 24 + 2/3 = 26/3

    To find a new numerator:
    a) Multiply the whole number 8 by the denominator 3. Whole number 8 equally 8 * 3/3 = 24/3
    b) Add the answer from previous step 24 to the numerator 2. New numerator is 24 + 2 = 26
    c) Write a previous answer (new numerator 26) over the denominator 3.

    Eight and two thirds is twenty-six thirds
  2. Conversion a mixed number 3 5/7 to a improper fraction: 3 5/7 = 3 5/7 = 3 · 7 + 5/7 = 21 + 5/7 = 26/7

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 7. Whole number 3 equally 3 * 7/7 = 21/7
    b) Add the answer from previous step 21 to the numerator 5. New numerator is 21 + 5 = 26
    c) Write a previous answer (new numerator 26) over the denominator 7.

    Three and five sevenths is twenty-six sevenths
  3. Subtract: 26/3 - 26/7 = 26 · 7/3 · 7 - 26 · 3/7 · 3 = 182/21 - 78/21 = 182 - 78/21 = 104/21
    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, 7) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 7 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - twenty-six thirds minus twenty-six sevenths = one hundred four twenty-firsts.

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:

  • Gingerbread house
    pernikova_ch Janka and Marienka calculated that there are 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house?
  • Clarissa
    books Clarissa read 1/2 of a book in the morning, and she read some more at night. By the end of the day, she still had 1/3 of the book left to read. How much of the book did Clarissa read at night?
  • Fraction expression
    fractions Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
  • Translate 2
    three_circles_inside_one Translate the given phrases to mathematical phrases. Thrice the sum of three fifths and two thirds less one half is what number?
  • Maria 3
    clocks Maria spent two eighths of her holiday in Town A, two fifth in Town B and the rest on travelling. What fraction of her holiday did she spend on travelling?
  • Evaluate 17
    fractions Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.
  • Bus vs train
    Clock0400 Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out?
  • There 14
    skola There are 250 people in a museum. 2/5 of the 250 people are girls 3/10 of the 250 people are boys The rest of the 250 people are adults Work out the number of adults in the museum.
  • When 5
    fractions When 5 is subtracted from both my numerator and denominator I become 3/4. What fraction i am?
  • Difference of two fractions
    subaru1 What is the difference between 1/2 and 1/6? (Write the answer as a fraction in lowest terms. )
  • Michael
    chocholate Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
  • Mother 7
    mangoes Mother bought 18 fruits. 1/3 were pineapple and the rest  were mangoes . how many were mangoes
  • 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?


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