Maharashtra State BoardSSC (English Medium) 6th Standard
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Types of Fraction - Improper Fraction and Mixed Fraction

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Topics

description

  • Improper Fraction
  • Mixed Fraction 
  • Conversion between Improper and Mixed fraction

definition

Improper Fraction: The fractions, where the numerator is greater than the denominator are called improper fractions i.e., numerator > denominator. `3/2, 12/7, 18/5` are all examples of improper fractions.

Mixed Fraction: A mixed fraction has a combination of a whole and apart. `3 2/3, 4 1/4, 3 7/8` are all examples of mixed fractions.

notes

Improper Fraction and Mixed Fraction:

1. Improper Fraction:

  • The fractions, where the numerator is greater than the denominator are called improper fractions i.e., numerator > denominator.
  • Thus, fractions like `3/2, 12/7, 18/5` are all improper fractions.

2. Mixed Fraction:

  • A mixed fraction has a combination of a whole and apart.
  • Thus, fractions like `3 2/3, 4 1/4, 3 7/8` are all mixed fractions.
  • Mixed fraction will be written as `"Quotient" ("Reminder"/"Divisor")`.

3. Interconversion between Improper and Mixed fraction:

i) Improper to mixed fraction:

1. `17/4 = (16 + 1)/4 = 16/4 + 1/4 = 4 + 1/4 = 4 1/4`.

 

i.e., 4 whole and `1/4  "more, or"  4 1/4`.

2. `11/3 = (9 + 2)/3 = 9/3 + 2/3 = 3 2/3`.

i.e., 3 whole and `2/3  "more, or"  3 2/3`.

3. `28/5 = (25 + 3)/5 = 25/5 + 3/5 = 5 + 3/5 = 5 3/5`

4. `19/6 = (18 + 1)/6 = 18/6 + 1/6 = 3 + 1/6 = 3 1/6`.

Thus, we can express an improper fraction as a mixed fraction by dividing the numerator by denominator to obtain the quotient and the remainder. Then the mixed fraction will be written as  `"Quotient" ("Reminder"/"Divisor")`

ii) Mixed to Improper Fraction:

1. `10 3/5 = ((5 × 10) + 3)/5 = 53/5`.

2. `9 3/7 = ((7 × 9) + 3)/7 = 66/7`.

3. `8 4/9 = ((8 × 9) + 4)/9 = 76/9`.

Thus, we can express a mixed fraction as an improper fraction as

`(("Whole" × "Denominator") + "Numerator")/"Denominator"`.

or

`"Quotient × Divisor + Reminder"/"Divisor"`.

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Mixed Fraction [00:01:38]
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