Back to Course

JSS2: MATHEMATICS - 1ST TERM

0% Complete
0/0 Steps
  1. Properties of Whole Numbers I | Week 1
    4Topics
    |
    2 Quizzes
  2. Properties of Whole Numbers II | Week 2
    4Topics
    |
    2 Quizzes
  3. Properties of Whole Numbers III | Week 3
    4Topics
    |
    1 Quiz
  4. Indices | Week 4
    2Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1Topic
    |
    1 Quiz
Lesson 5, Topic 1
In Progress

Law 1: Multiplication Law

Lesson Progress
0% Complete

Law 1:  Multiplication law

\( \scriptsize a^m \: \times \: a^n = a^{m \:+ \:n} \)

This law applies only when numbers have the same base number.

Note: 23 and 24 have the same base number, 2, while 54 and 61 do not have the same base number because 5 and 6 are different.

e.g

23 x 24   =  23+4   =  27

23 x 34   =   2 x 33+4   (incorrect)

Example 1 (Using the Multiplication Law)

Simplify the following 

a. 25  x 24

b. c5  x c4

c. a2 x a7

d. 52 x 53 x 54

e. 72 x 72 x 73

Solution

a. 25 x 24   

=  25+4  

= 29

(same base ‘2’)

b. c5 x c4    

=    c5+4 

=  c9

(same base ‘c’)

c. a2 x a7    

=  a2 + 7  

=  a9

(same base ‘a’)

d. 52 x 53 x 54 

=  52+3+4  

=  59

(same base ‘5’)

e. 72 x 72 x 73   

=   72+2+3 

=  77

(same base ‘7’)

Example 2

Simplify the following by expanding the terms

a. 25 x 24

b. 52 x 53 x 54

c. c5 x c4

d. a2 x a7

e. 72 x 72 x 73

Solution

a. 25 x 24   

= (2 x 2 x 2 x 2 x 2)  x (2 x 2 x 2 x 2)  

=  29

b. 52 x 53 x 54

= (5 x 5) x (5 x 5 x 5 ) x (5 x 5 x 5 x 5)

=  59

c. c5 x c

= (c x c x c x c x c)  x (c x c x c x c)

=  c9

d. a2 x a 

= (a x a)  x (a x a x a x a x a x a x a)

=  a9

e. 72 x 72 x 7

= (7 x 7) x (7 x 7) x (7 x 7 x 7)

= 7 x 7 x 7 x 7 x 7 x 7 x 7 

= 77

Example 3

Simplify the following;

a. \( \scriptsize 2f^2 \: \times \: 3f^3 \)

b. \( \frac{1}{2} \scriptsize y^2 \: \times \: 4y^2 \: \times \: y^3 \)

c. \( \scriptsize 10k^2 \: \times \: 2k^3 \)

Solution

a. \( \scriptsize 2f^2 \: \times \: 3f^3 \\ \scriptsize = 2 \: \times \: 3 \: \times \: f^2 \: \times \: f^3 \\ \scriptsize = 6 \: \times \: f^{2\:+\:3} \\ \scriptsize= 6 \: \times \: f^5 \\ \scriptsize = 6f^5 \)

b. \( \frac{1}{2} \scriptsize y^2 \: \times \: 4y^2 \: \times \: y^3 \\ = \frac{1}{2} \scriptsize \: \times \: y^2 \: \times \: 4 \: \times \:y^2 \: \times \: y^3 \\ = \frac{1}{2} \scriptsize \: \times \: 4 \: \times \: y^2 \: \times \:y^2 \: \times \: y^3 \\ =\scriptsize 2 \: \times \: y^{2+2+3} \\ = \scriptsize 2 \: \times \: y^7 \\ \scriptsize = 2y^7\)

c. \( \scriptsize 10k^2 \: \times \: 2k^3 \\ \scriptsize = 10 \: \times \: 2 \: \times \: k^2 \: \times \: k^3 \\ \scriptsize = 20 \: \times \: k^{2+3} \\ \scriptsize = 20k^5 \)

d. \(\scriptsize y \: \times \: \frac{1}{2}y^2 \: \times \: y^3 \\ \scriptsize = \frac{1}{2} \: \times \: y \: \times \: y^2 \: \times \: y^3 \\ \scriptsize = \frac{1}{2} \: \times \: y^{1+2+3} \\ \scriptsize = \frac{1}{2}y^6\)

back-to-top
error: