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:

1 4/11 / 3 3/5 = 25/660.3787879

Spelled result in words is twenty-five sixty-sixths.

How do you solve fractions step by step?

  1. Conversion a mixed number 1 4/11 to a improper fraction: 1 4/11 = 1 4/11 = 1 · 11 + 4/11 = 11 + 4/11 = 15/11

    To find new numerator:
    a) Multiply the whole number 1 by the denominator 11. Whole number 1 equally 1 * 11/11 = 11/11
    b) Add the answer from previous step 11 to the numerator 4. New numerator is 11 + 4 = 15
    c) Write a previous answer (new numerator 15) over the denominator 11.

    One and four elevenths is fifteen elevenths
  2. Conversion a mixed number 3 3/5 to a improper fraction: 3 3/5 = 3 3/5 = 3 · 5 + 3/5 = 15 + 3/5 = 18/5

    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 3. New numerator is 15 + 3 = 18
    c) Write a previous answer (new numerator 18) over the denominator 5.

    Three and three fifths is eighteen fifths
  3. Divide: 15/11 : 18/5 = 15/11 · 5/18 = 15 · 5/11 · 18 = 75/198 = 3 · 25 /3 · 66 = 25/66
    Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 18/5 is 5/18) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 3 gives 25/66.
    In words - fifteen elevenths divided by eighteen fifths = twenty-five sixty-sixths.

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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  • The third
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  • Pumps
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  • Mrs. Glover
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  • Product of two fractions
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  • A baker
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  • Balls
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  • Almonds
    almonds Rudi has 4 cups of almonds. His trail mix recipe calls for 2/3 cup of almonds. How many batches of trail mix can he make?
  • The bird
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  • Curtain 3
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  • Mario 2
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