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:

16 3/9 - 10 2/5 = 89/15 = 5 14/15 ≅ 5.9333333

Spelled result in words is eighty-nine fifteenths (or five and fourteen fifteenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 16 3/9 to a improper fraction: 16 3/9 = 16 3/9 = 16 · 9 + 3/9 = 144 + 3/9 = 147/9

    To find new numerator:
    a) Multiply the whole number 16 by the denominator 9. Whole number 16 equally 16 * 9/9 = 144/9
    b) Add the answer from previous step 144 to the numerator 3. New numerator is 144 + 3 = 147
    c) Write a previous answer (new numerator 147) over the denominator 9.

    Sixteen and three ninths is one hundred forty-seven ninths
  2. Conversion a mixed number 10 2/5 to a improper fraction: 10 2/5 = 10 2/5 = 10 · 5 + 2/5 = 50 + 2/5 = 52/5

    To find new numerator:
    a) Multiply the whole number 10 by the denominator 5. Whole number 10 equally 10 * 5/5 = 50/5
    b) Add the answer from previous step 50 to the numerator 2. New numerator is 50 + 2 = 52
    c) Write a previous answer (new numerator 52) over the denominator 5.

    Ten and two fifths is fifty-two fifths
  3. Subtract: 147/9 - 52/5 = 147 · 5/9 · 5 - 52 · 9/5 · 9 = 735/45 - 468/45 = 735 - 468/45 = 267/45 = 3 · 89/3 · 15 = 89/15
    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 the both denominators - LCM(9, 5) = 45. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 5 = 45. In the next intermediate step , cancel by a common factor of 3 gives 89/15.
    In words - one hundred forty-seven ninths minus fifty-two fifths = eighty-nine fifteenths.

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:

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    meter_11 Express in mm: 5 3/10 cm - 2/5 mm
  • Add sub fractions
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  • School
    skola_16 There are 150 pupils in grade 5 . 2/3 of it are female. By what fractions are the males?
  • 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?
  • Find the 24
    plusminus_1 Find the difference between 2/7 and 1/21
  • Akpan
    clocks2 Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week?
  • Pupils 7
    skola_4 There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls?
  • Michael
    chocholate Michael had a bar if chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?


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