Fraction calculator

Work with fractions

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 1/6 / 1 7/8 = 196 / 45 = 4 16 / 45 ≅ 4.3555556

Spelled result in words is one hundred ninety-six forty-fifths (or four and sixteen forty-fifths).

How do you solve fractions step by step?

  1. Conversion a mixed number 8 1 / 6 to a improper fraction: 8 1/6 = 8 1 / 6 = 8 · 6 + 1 / 6 = 48 + 1 / 6 = 49 / 6

    To find a new numerator:
    a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6 / 6 = 48 / 6
    b) Add the answer from previous step 48 to the numerator 1. New numerator is 48 + 1 = 49
    c) Write a previous answer (new numerator 49) over the denominator 6.

    Eight and one sixth is forty-nine sixths

  2. Conversion a mixed number 1 7 / 8 to a improper fraction: 1 7/8 = 1 7 / 8 = 1 · 8 + 7 / 8 = 8 + 7 / 8 = 15 / 8

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8 / 8 = 8 / 8
    b) Add the answer from previous step 8 to the numerator 7. New numerator is 8 + 7 = 15
    c) Write a previous answer (new numerator 15) over the denominator 8.

    One and seven eighths is fifteen eighths

  3. Divide: 49 / 6 : 15 / 8 = 49 / 6 · 8 / 15 = 49 · 8 / 6 · 15 = 392 / 90 = 2 · 196 / 2 · 45 = 196 / 45
    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 15 / 8 is 8 / 15 ) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 196 / 45 .
    In other words - forty-nine sixths divided by fifteen eighths = one hundred ninety-six forty-fifths.

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:

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