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Fractions

    Improper and Mixed Fractions

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6th class > Fractions > Improper and Mixed Fractions

Improper and Mixed Fractions

Anagha, Ravi, Reshma and John shared their tiffin. Along with their food, they had also, brought 5 apples. After eating the other food, the four friends wanted to eat apples.

Split the 5th apple and distribute to four of them

Ravi
Reshma
Anagha
John

How can they share five apples among four of them?

Anagha said, ‘Let each of us have full apple and a of the fifth apple.’

Reshma said, ‘That is fine, but we can also divide each of the five apples into the 4 equal parts and take one-quarter from each apple’

Ravi said, ‘In both the ways of sharing, each of us would get the same share, i.e., 5 quarters. Since 4 quarters make one whole, we can also say that each of us would get 1 whole and one quarter. The value of each share would be five divided by four. Is it written as 5÷4?’ John said, ‘Yes the same as 54’. Reshma added that in 54, the numerator is bigger than the denominator. The fractions, where the numerator is bigger than the denominator are called improper fractions. Thus, fractions like 32,127,185 are all improper fractions.

Given the sample examples below try to draw the improper fractions like 52, 61,73

Ravi reminded John, ‘What is the other way of writing the share? Does it follow from Anagha’s way of dividing 5 apples?’

John nodded, ‘Yes, It indeed follows from Anagha’s way. In her way, each share is one whole and one quarter. It is 1 + 14 and written in short as 1 + 14. Remember, 1 + 14 is the same as .

Recall the apples eaten by Farida. She got 2 x 12 poories ( depicted in the below figure) i.e.

How many shaded halves are there in 2 x 12? There are shaded halves.

So, the fraction can also be written

as 52. Thus, 2 x 12 is the same as 52.

Fractions such as 1 x 14 and 2 x 12 are called Mixed Fractions. A mixed fraction has a combination of a whole and a part. It is another way of representing improper fractions.

Now, let's learn how to convert imporper to mixed farction and vice-versa.

Converting improper fraction to mixed fraction:

174

  • Finding the nearest multiple of the denominator(4) to the numerator(17) i.e.
  • Rewriting the numerator as a sum
  • splitting the given fraction into two separate fractions
  • simplifying the possible terms
  • Removing the addition sign, we get the desired mixed fraction.

What about the inverse of this: converting mixed fractions into improper fractions

Let's try it.

Converting mixed fraction into an improper fraction:

234

  • Insert the addition sign in between the whole number(2) and fraction(3/4).
  • We can rewrite the whole number by writing it as a fraction
  • Taking the LCM of the two denominators and re-writing the whole number
  • Evaluating the first term is
  • Writing the numerator as a sum
  • Adding the values are
  • Therefore the fraction is

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

(Whole x Denominator) + NumeratorDenominator

Using the above method, try solving the below related problems.

Let's Solve