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 1/4 - 3 2/5 - (2 1/3 - 1/4) = 83/30 = 2 23/30 ≅ 2.7666667

Spelled result in words is eighty-three thirtieths (or two and twenty-three thirtieths).

How do you solve fractions step by step?

  1. Conversion a mixed number 8 1/4 to a improper fraction: 8 1/4 = 8 1/4 = 8 · 4 + 1/4 = 32 + 1/4 = 33/4

    To find new numerator:
    a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/4 = 32/4
    b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
    c) Write a previous answer (new numerator 33) over the denominator 4.

    Eight and one quarter is thirty-three quarters
  2. Conversion a mixed number 3 2/5 to a improper fraction: 3 2/5 = 3 2/5 = 3 · 5 + 2/5 = 15 + 2/5 = 17/5

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
    b) Add the answer from previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
    c) Write a previous answer (new numerator 17) over the denominator 5.

    Three and two fifths is seventeen fifths
  3. Subtract: 33/4 - 17/5 = 33 · 5/4 · 5 - 17 · 4/5 · 4 = 165/20 - 68/20 = 165 - 68/20 = 97/20
    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(4, 5) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - thirty-three quarters minus seventeen fifths = ninety-seven twentieths.
  4. Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
    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 3.

    Two and one third is seven thirds
  5. Subtract: 7/3 - 1/4 = 7 · 4/3 · 4 - 1 · 3/4 · 3 = 28/12 - 3/12 = 28 - 3/12 = 25/12
    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, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - seven thirds minus one quarter = twenty-five twelfths.
  6. Subtract: the result of step No. 3 - the result of step No. 5 = 97/20 - 25/12 = 97 · 3/20 · 3 - 25 · 5/12 · 5 = 291/60 - 125/60 = 291 - 125/60 = 166/60 = 2 · 83/2 · 30 = 83/30
    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(20, 12) = 60. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 20 × 12 = 240. In the next intermediate step, , cancel by a common factor of 2 gives 83/30.
    In words - ninety-seven twentieths minus twenty-five twelfths = eighty-three thirtieths.

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:

  • Length subtracting
    meter_11 Express in mm: 5 3/10 cm - 2/5 mm
  • Add sub fractions
    fractions_2 What is 4 1/2+2/7-213/14?
  • Pizza fractions
    pizza Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • School
    skola_16 There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males?
  • Fractions mul add sum
    fractions_3 To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Difference mixed fractions
    mixed_fractions_1 What is the difference between 4 2/3 and 3 1/6?
  • Cake fractions
    dort Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
  • Pounds
    jablka_8 3 pounds subtract 1/3 of a pound.
  • Employees
    workers_45 Of all 360 employees, there are 11/12 women. How many men work in a company?
  • 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?
  • Forty
    skola_2 Forty five of the 80 students were girls. What is the ratio of girls to boys?
  • Find the 24
    plusminus_1 Find the difference between 2/7 and 1/21
  • Coloured teacups
    venn The teacups in Tea Stop 55 are `2/5` green and `3/10` yellow. What fraction of the teacups are neither green nor yellow?


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