Fractions (Introduction)
A fraction is a number representing part of a whole. The whole may be a single object or a group of objects.
For example
5/12 is a fraction. It is read as “five-twelfths”.
Here “12” stand for the number of equal parts into which the whole has been divided. It is called the denominator.
And “5” stand for the number of equal parts which have been taken out. It is called numerator.
Facts
1. A fraction is part of a whole. It is less than 1 whole thing, but more than 0.
2. The parts have to be equal.
3. Every fraction has two parts: a top number called numerator and a bottom number called denominator.
Example 1: Write the fraction representing the shaded portion.
Example 2: Identify the error, if any.
Is this figure represents ¼?
Solution: The given figure do not represent fraction ¼ because the shape is not equally divided.
Example 3: What fraction of a day is 5 hours?
Solution: There are 24 hours in a day.
Therefore, 5 hours of a day represent
Example 4: Thomas has brought two types of chocolate. He shared his chocolates with his two friends, in such a way that each of them will have an equal share.
i. How can Thomas divide his chocolates so that each one has an equal share?
ii. What part of a chocolate will each boy receive?
Solution:
i. Thomas will divide each type of chocolates in three equal parts. So, that each will get one part of both chocolates.
ii. Each will receive 1/3 part of each chocolate.
Example 5: Write the natural numbers from 40 to 50. What fraction of them are prime numbers?
Solution: Natural numbers from 40 to 50 = 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.
Prime numbers among these numbers are = 41, 43, 47
Therefore, out of 11 numbers, 3 are prime numbers.
So, Fraction 3/11 represents prime numbers.
Example 6: Diva bought 3 gel pens and received 5 others as gifts on her birthday. What fraction of her total gel pens did she buy and what fraction did she receive as gifts?
Solution: Total number of gel pens she had = 3 + 5 = 8
Fraction of her total gel pens that she bought = 3/8
Fraction of her total gel pens that she received as gifts = 5/8
Example 7: A bag contains 60 marbles. Out of which 20 are red in color and 40 are blue in color.
i. What fraction of marbles is red in colors?
ii. What fraction of marbles is blue in colors?
Solution: Total marbles = 60
Red marbles = 20
Blue marbles = 30
i. Fraction of red marbles = 20/60
ii. Fraction of blue marbles = 30/60