A simple code

Subject : Mathematics

Topic : A simple code

Class : JSS 1

Lesson : 2 Content

Code system is an interesting aspect of number manipulation . Here, the alphabets A— Z are allocated the numbers 1—26 respectively . This gives a simple code as shown below:

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 J 10 K 11 L 12 M 13
N 14 O 15 P 16 Q 17 R 18 S 19 T 20 U 21 V 22 W 23 X 24 Y 25 Z 26

Example 1

What does ( 14,9,7,5,18,9,1) mean using the above code ?. Solution : 14 = N ; 9 = I ; 7 = G ; 5 = E ; 18 = R ; 9 = I ; 1 = A . Therefore ; (14 , 9 , 7 ,5 ,18, 9 ,1) = NIGERIA

Example 2

Translate INTERNATIONAL into simple code using the table above . Solution

I = 9 ; N = 14 ; T = 20 ; E = 5 ; R = 18; N = 14 ; A = 1; T = 20 ; I = 1; O = 15; N =14; A = 1; L = 12 Therefore , INTERNATIONAL = (9 , 14 , 20 , 5 , 18 ,14 , 1 , 20 , 1 , 15 , 14 , 1 , 12) ASSIGNMENT A

Use the above table to translate the following :

(1 ) (1 ,2, 21, 10 ,11) (2) (1 , 9 ,18 ,16 , 15 ,18 ,20) .

(3) (20 ,8 ,5 ) (13 ,1 ,18 ,11 ,5 ,20 ) (4) (12 ,1 ,7 ,15 ,19) (14 ,9 ,7 ,5 ,18 ,9 1)

(5) ( 1 ,12 ,12 ) ( 9 ,19 ) ( 23 , 5 , 12 ,12)

Translate the following into simple code using the above table.

(6) GOOD NIGHT (7) DEMOCRACY (8) SAFE FUEL (9) BIRTHDAY (10) UNLIMITED

Topic : Factors and multiples .

Sub topic: Factors and prime numbers. CONTENTS

Factors are numbers that divide a given number without a remainder. The numbers we multiply together to get a product are factors of the product .

Example

List all the factors of (i) 24 ( ii) 56 . SOLUTION

(i) 24 = 1 X 24, 24 = 2 X 12 ; 24 = 3 X 8; 24 = 4 X 6 .

Therefore , factors of 24 are : 1 , 2, 3, 4 ,6 ,8 ,12 ,24 .

(ii) 56 = 1 x 56 , 56 = 2 x 28, 56 = 4 x 14 , 56 = 7 x 8 .

Therefore, factors of 56 are: 1 , 2 , 4 , 7 , 8 , 14 ,28 ,56 . PRIME NUMBERS

Any number that has only itself and 1 as factors is called a prime number . The first ten prime numbers are : 2,3,5,7,11.13,17,19,23 and 29. (Note: 1 is not a prime number)

NOTE : Prime numbers cannot be divided by any other number except itself and 1 . ASSIGNMENT B

  1. List all the factors of : (a) 18 (b) 27 (c) 36 (d) 54 (e) 60 .
  2. Write down all the prime numbers between 30 and 50

TOPIC : Prime factors

The prime factors of a number are the factors of the number that are prime. For example, factors of 56 are : 1,2,4,7,8,14,28,56 . Out of these only 2 and 7 are prime, therefore 2 and 7 are the prime factors of 56.

We can write every non-prime numbers as a product of prime factors : For example , 24 = 2 x 2 x 2 x 3.

To find the prime factors of a number :

Start with the smallest prime number, 2 . Find out if this will divide the number without any remainder. If it will not divide try the next prime number,3 and continue with the rest prime numbers.

NOTE : If a prime number will divide , check if it will divide again before moving on to the next prime.

Example

Express 252 as a product of prime factors .

SOLUTION

2 252
2 126
3 63
3 21
7 7
1

Therefore , 252 = 2 x2 x 3 x3 x7 . ASSIGNMENT C

(1) use the above method to express the following as products of prime factors : (1) 28 (2) 72 (3) 84 (4) 180 (5) 288 .

 

 

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