Lesson2

grade 7

1. Chapter IChapter I
Real Numbers Real Numbers
Lesson 2
Number Theory

2. If the name MALOU is written continously
without gap, what is the 2013
th
letter?

3. Division of Real NumbersDivision of Real Numbers

Rational Numbers Irrational Numbers
Whole
Nos.
Nos. that are not
rational or cannot
be expressed in
the fraction form.
DecimalsIntegers Non-Terminating /
Non-Repeating
Decimals
Nos. that can be
expressed as fraction
whose denominator is
not zero.
Fractions
Counting Nos.

4. Answer the followingAnswer the following
When is a number considered rational?
If the number can be expressed in the
form a/b, where b ≠ 0.
When is it considered irrational?
If the number can not be expressed in
the form a/b, where b ≠ 0.

5. What is the opposite of prime numbers?
Ans. composite numbers
Show that 12 is even.
To show that a number is even,
show that the number is divisible by
2 by expressing it in the form 2n.
Answer: 12 is even because it can be
written as 2(6).

6. Prove that 8 is rational.
8 is rational because it can be written
in the form .
Is 0.75 rational? Prove or disprove.
0.75 is rational since it can be written
as fraction form .
1
8
4
3

7. Whole NumbersWhole Numbers
Whole Numbers
{0, 1, 2, 3,4, 5,6……..}
Natural or Counting Nos.
{1, 2, 3,4 ,5, ………}
Set of Even Nos. – {2, 4, 6, 8,10……}
Set of Odd Nos. – {1, 3, 5, 7,9,…….}
Set of Prime Nos. – {2, 3, 5, 7, 11……}
When is a number considered prime?
A no. is prime if it has only two
factors, 1 and the number itself.

8. To show that a number is even:
Express the number in the form 2n or
show that 2 is a factor of the number.
Show that 18 is an even no.
18 = 2(9)  hence, 18 is even.

9. Show that 27 is an odd number.
To show that a number is odd, express
the number in the form (even+1) or
(2n+1) or (2n – 1).
27 is odd since 27 = 2(13) + 1 or
= 2(14) – 1
List all prime numbers from 1 to 100.
2 3 5 7 11 13 17 19
23 29 31 37 41 43 47 53
59 61 67 71 73 79 83 89 97

10. Factors and MultiplesFactors and Multiples
If a, b and c are real numbers and
1. a x b = c, then a and b are factors of
c.
Example: 3 x 2 = 6
hence, 3 and 2 are factors of 6.
Also,
2. If a x b = c, then, c is a multiple of a
and b .
Hence, 6 is a multiple of 2 and 3.

11. Answer the followingAnswer the following
1. Is 8 a factor of 4? Why / Why not?
2. What are factors of 4?
3. Is 5 a multiple of 10? Why/Why not?
4. When will you say that a number is a
multiple of 10?
5. Give the smallest common multiple of
3 and 4?
6. List all factors of 18.
7. Show that 38 is an even number.
8. Enumerate the prime numbers between 40
and 60.
9. Show that 0.25 is a rational number.
10. When is a number divisible by 9?

12. 11. Mike said, 91 is a prime number. Do
you
agree? Explain.
12. Every decimal number is rational number.
True or false. Explain.
13. Explain the difference between rational
and irrational, prime and composite and
GCF and LCM of numbers.
14. How many numbers less than 50 are
divisible by 3 or 4?

13. 15. What is the smallest positive number
greater than 1 that will give a remainder of
1 when divided by 2, 3, 4, 5, 6, 7, 8, and 9?
16. Red lights flash every 5 seconds, green
every 4 sec, blue and yellow every 3 sec. If
the lights flash together at 6pm, when will
they flash again together?

14. There are 100 students and 100 lockers along
the hallway. All lockers are closed. The first
student goes to every locker and opens all.
The second student goes to every second
locker and closes the locker. The third
student goes to every third locker and opens
it if it is close or closes it if it is open. The
fourth student goes to every fourth locker
and again closes it if open or open it if close.
The pattern continuous with the fifth, sixth,
etc. student. After all 100 students have
gone through the lockers, how many lockers
are left open?