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JSS2: MATHEMATICS - 1ST TERM

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  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 2
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Law 2: Division Law

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\( \scriptsize a^m \div a^n = a^{m \: – \: n} \)

Similar to the Multiplication Law, the Division Law applies only when we have numbers with the same base numbers. 

e.g.

27 ÷ 22 

= 27-2

= 25

By expansion:

= \(\scriptsize 2^7 \: \div \:2^2 \\= \frac{2^7}{2^2} \\ = \frac{2 \: \times \: 2 \: \times \: 2\: \times \: 2\: \times \: 2\: \times \: 2\: \times \: 2}{2 \: \times \: 2}\\ = \frac{2 \: \times \: 2 \: \times \: 2\: \times \: 2\: \times \: 2\: \times \: \not{2}\: \times \: \not{2}}{\not{2}\: \times \: \not{2}}\\ \scriptsize = 2^5\)

Example 1

Simplify the following by expansion

a. 76 ÷ 72

b. m9 ÷ m4

c. x7 ÷ x4

d. h10 ÷ h4

e. 1312 ÷139

f. 18h5 ÷ 9h4

g. 3x2 ÷ 21x7

Solution

a. \(\scriptsize 7^6 \: \div \:7^2 \\= \frac{7^6}{7^2} \\ = \frac{7 \: \times \: 7 \: \times \: 7\: \times \: 7\: \times \: \not{7}\: \times \: \not{7}}{\not{7} \: \times \: \not{7}}\\ \scriptsize = 7^4\)

b. \(\scriptsize m^9 \: \div \:m^4 \\= \frac{m^9}{m^4} \\ =\scriptsize \frac{m \: \times \: m \: \times \: m\: \times \: m\: \times \: m\: \times \: m\: \times \: m\: \times \: \not{m}\: \times \: \not{m}}{\not{m} \: \times \: \not{m}\: \times \: \not{m}\: \times \: \not{m}}\\ \scriptsize = m^5\)

c. \(\scriptsize x^7 \: \div \:x^4 \\= \frac{x^7}{x^4} \\ = \frac{x \: \times \: x \: \times \: x\; \times \: \not{x}\: \times \:\not{ x}\: \times \: \not{x}\: \times \: \not{x}}{\not{x} \: \times \: \not{x}\: \times \: \not{x}\: \times \: \not{x}}\\ \scriptsize = x^3\)

d. \(\scriptsize h^{10} \: \div \:h^4 \\= \frac{h^{10}}{h^4} \\ = \frac{h \: \times \: h \: \times \: h \: \times \: h \: \times \: h \: \times \:h\: \times \: \not{h} \: \times \:\not{ h}\: \times \: \not{h}\: \times \: \not{h}}{\not{h} \: \times \: \not{h}\: \times \: \not{h}\: \times \: \not{h}}\\ \scriptsize = h^6\)

e. \(\scriptsize 13^{12} \: \div \:13^9 \\= \frac{13^{12}}{13^9} \\ =\scriptsize \frac{13 \: \times \: 13 \: \times \: 13 \: \times \: \not{13} \: \times \: \not{13} \: \times \:\not{13} \: \times \: \not{13} \: \times \: \not{13}\: \times \: \not{13}\: \times \: \not{13} \: \times \: \not{13} \: \times \: \not{13}}{\not{13} \: \times \: \not{13}\: \times \: \not{13}\: \times \: \not{13} \: \times \: \not{13} \: \times \: \not{13}\: \times \: \not{13}\: \times \: \not{13} \: \times \: \not{13}}\\ \scriptsize = 13^3\)

f. \(\scriptsize 18 h^{5} \: \div \: 9 h^4 \\= \frac{18h^{5}}{9h^4} \\ = \frac{18 \: \times \: h \: \times \: \not{h} \: \times \: \not{h} \: \times \: \not{h} \: \times \: \not{h} }{9 \: \times \: \not{h} \: \times \: \not{h}\: \times \: \not{h}\: \times \: \not{h}}\\ \scriptsize = 2h\)

g. \( \scriptsize 3x^2 \: \div \: 21x^7 \\ = \frac{3x^2}{21x^7} \\ = \frac{3 \: \times \: \not{x} \: \times \: \not{x}}{21 \: \times \: x \: \times \: x \: \times \: x \: \times \: x \: \times \: x\: \times \: \not{x} \: \times \: \not{x}} \\ = \frac{1}{7x^5} \)

Example 2

Simplify the following by the law of indices

a. 76 ÷ 72 

= 76-2 

= 74

same base

b. m9 ÷ m4

= m9-4

=  m5

same base

c. x7 ÷ x4 

= x7-4 

= x3

same base

d. h10 ÷ h4  

=  h10-4  

=  h6

same base

e. 1312 ÷ 13

=  1312-9  

=  133

same base

f. 18h5 ÷ 9h4  

\(= \frac{18h^8}{9h^4}\\ = \scriptsize 2h^{5\:-\:4}\\ = \scriptsize 2h^1 \\= \scriptsize 2h  \)

same base

g. 3x2 ÷ 21x7

=   \( \frac{3}{21} \scriptsize x^2 \: \div \: x^7 \\=  \frac{3}{21} \scriptsize x^{2 \: -\: 7}\\ = \frac{1}{7} \scriptsize x^{-5} \)

same base  

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