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.
How can they share five apples among four of them?
Anagha said, ‘Let each of us have
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
John said, ‘
Reshma added that in
Thus, fractions like
Given the sample examples below try to draw the improper fractions like
1. Write five improper fractions with denominator 7.
2. Write five improper fractions with numerator 11.
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 +
Remember, 1 +
Recall the apples eaten by Farida. She got 2 x
How many shaded halves are there in 2 x
There are
So, the fraction can also be written as
Fractions such as 1 x
Now, let's learn how to convert imporper to mixed farction and vice-versa.
Express the following as mixed fractions.
(i)
- Finding the nearest multiple of the denominator(4) to the numerator(17) i.e.
- Rewriting the numerator as a sum: 17 = 16 +
- Splitting the given fraction into two separate fractions
- Simplifying the possible terms
- Removing the addition sign, we get the desired mixed fraction.
- We have the desired answer.
(ii)
- Finding the nearest multiple of the denominator(3) to the numerator(11) i.e.
- Rewriting the numerator as a sum: 11 = 9 +
- Splitting the given fraction into two separate fractions
- Simplifying the possible terms
- Removing the addition sign, we get the desired mixed fraction.
- We found the answer.
(iii)
- Finding the nearest multiple of the denominator(5) to the numerator(27) i.e.
- Rewriting the numerator as a sum: 27 = 25 +
- splitting the given fraction into two separate fractions
- simplifying the possible terms
- Removing the addition sign, we get the desired mixed fraction.
- We found the answer.
(iv)
- Finding the nearest multiple of the denominator(3) to the numerator(7) i.e.
- Rewriting the numerator as a sum: 7 = 6 +
- Splitting the given fraction into two separate fractions
- Simplifying the possible terms
- Removing the addition sign, we get the desired mixed fraction.
- We found the answer.
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 =
Express the following mixed fractions as improper fractions.
- 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