Page 159 - Ganit Kaushal

9. Assertion (A): 9 × 7 = 7 × 9 = 63

Reason (R): If ‘a’ and ‘b’ are any two whole numbers, then a × b = b × a.
Case Study Based Questions
1. There are 30 students in the class. 15 students from a nearby slum area have taken admission in the
school in standard VI. To meet the nutritional needs of these children, the students of Standard X
decided to bring fruits for them as per the following plan.
(i) Students with roll numbers less than or equal to 15 and being composite numbers: fruits for the
first week.
(ii) Students with roll numbers greater than 15 and composite numbers: fruits for the second week.
(iii) Students with roll numbers less than or equal to 15 and being prime numbers: fruits for the
third week.
(iv) Students with roll numbers greater than 15 and being prime numbers: fruits for the 4th week.

Based on the above information answer the following questions:
(a) How many students brought fruits in the first and second weeks?
(b) How many students brought fruits in the 3rd and 4th weeks?
(c) The date of birth of one student is 22-11-2010. When written as 22, 11, 20, 10; how many
composite numbers are there?
(d) How many students brought fruits in the first and fourth weeks?
(e) How many students brought fruits in the second and third weeks?

Summary of the Chapter

• Factors: A factor of a number is an exact divisor of that number. For example, 1, 2, 3, 4, 6, and 12 are
factors of 12. We can also say that the numbers 1, 2, 3, 4, 6 and 12 are exact divisors of 12.
• Multiples: The product obtained on multiplying two or more whole numbers is called a multiple of that
number or the numbers being multiplied. For example: The numbers 3, 6, 9, 12, and 15 are multiples of 3.
• Perfect number: A number for which the sum of all its factors is equal to twice the number is called
a perfect number.
• Prime and Composite Numbers: A prime number (or a prime) is a natural number greater than 1 that
has no positive divisors other than 1 and itself. A composite number is a number which has more than
two factors i.e., it can be completely divided by numbers other than 1 or itself.
• Even and Odd Numbers: An even number is defined as a whole number that is a multiple of 2. On the
other hand, a whole number that is not a multiple of 2 is called an odd number.
• Co-prime numbers: Numbers are co-prime if their highest common factor is 1. The only common
factor between co-prime numbers is 1. It is obvious that two prime numbers are also co-prime.
• Twin Prime numbers: The term twin primes is used for a pair of odd prime numbers that differ by two.
For example: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), etc. are twin prime pairs.

• Divisibility rules: Remember the divisibility rules given in Section 5.6 of this chapter.

Prime Time 157