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Math18

Mixed fraction

Content

What are mixed fractions?

A mixed fraction represents an integer and a proper fraction, in other words, corresponds to the sum of an integer plus a fractional part.

3
1
/
2

Where, 3 is the integer number and 1/2 is the proper fraction.

Note: A proper fraction is one in which its numerator is smaller than its denominator.

It is advisable to know the basic concepts of fractions to better understand the terms used and the operations that are presented.


How to solve mixed fractions?

Depending on the problem, a fraction can be represented as mixed or improper, for that reason you must first have the basic concepts to convert a mixed fraction to improper and vice versa from a proper fraction to a mixed one.

Note: An improper fraction is one in which its numerator is greater than the denominator.

If the number is given with an integer and decimals, the decimal part must first be converted to a fraction.

Conversion of improper to mixed fractions

Improper fractions can be represented as mixed fractions that are made up of a whole part and a fractional part.

For example, to convert the improper fraction 18/4 to a mixed fraction, the conversion is performed as follows:

  1. The fraction is divided.
          4 4  18     -16        2
  2. Once the division is made, the quotient indicates the whole part and the residue indicates the fractional part.
          4 ← quotient 4  18     -16        2 ← residue
  3. The fractional part is formed with the residue as numerator and with the divisor as denominator (the denominator is maintained).
    2
    /
    4
  4. The improper fraction, in this case 18/4 becomes a mixed fraction with 4 integers and 2/4.
    18
    /
    4
    = 4
    2
    /
    4

Conversion of mixed to improper fractions

Mixed fractions can be converted to improper fractions.

For example, to convert the mixed fraction 4 and 2/3 to an improper fraction, the conversion is performed as follows:

  1. The integer part is multiplied by the denominator of the fraction.
    4 x 3 = 12
  2. The result of the multiplication is added with the numerator of the fraction.
    12 + 2
    /
    3
  3. Once the multiplication and addition are done, the result is placed in the numerator and the denominator of the fraction remains the same.
    4
    2
    /
    3
    =
    14
    /
    3

Operations with mixed fractions

To be able to solve the operations of mixed fractions it is recommended to convert any mixed fraction to an improper fraction.

Sum of mixed fractions

To resolve, proceed to the following steps:

  1. Convert mixed fractions to improper.
  2. Perform the corresponding operation to solve the sum of fractions.

Subtraction of mixed fractions

To resolve, proceed to the following steps:

  1. Convert mixed fractions to improper.
  2. Perform the corresponding operation to solve the subtraction of fractions.

Multiplication of mixed fractions

To resolve, proceed to the following steps:

  1. Convert mixed fractions to improper.
  2. Perform the corresponding operation to solve the multiplication of fractions.

Division of mixed fractions

To resolve, proceed to the following steps:

  1. Convert mixed fractions to improper.
  2. Perform the corresponding operation to solve the division of fractions.