1.5 Division in algebra

Mathematics

Grade 8

The number system

(natural and whole numbers)

Module 6

Division in algebra

CLASS ASSIGNMENT 1

• Discover more and more about division in ALGEBRA!

• Write the following fraction in its simplest form in $\frac{\text{45}}{\text{36}}$ = ........................
• Like common fractions, you can also write algebraic fractions in the simplest form.

What would the following be in its simplest form? $\frac{{\mathrm{6a}}^{2}b}{3\text{ab}}$ = .........................

Yes, it is actually like this: $\frac{6\times a\times a\times b}{3\times a\times b}$ = $\frac{2\times a\times 1\times 1}{1\times 1\times 1}$

(Now you may cancel all the like terms above and below)(What remains above and below? Just write down the answer)

• There is a shortcut for terms with exponents: $\frac{m^5}{m^7}=$ .........................

Are you able to identify the shortcut? Yes, 7 - 5 = 2. Therefore m ² what remains below the line.

Answer : $\frac{1}{m^2}$

1. Now simplify the following:

1.1 $\frac{\text{18}{m}^5}{{\mathrm{9m}}^2}$ ..................................................

1.2 $\frac{\text{15}{p}^4{y}^7}{{\mathrm{3p}}^7{y}^3}$ ..................................................

1.3 $\frac{({\mathrm{4m}}^2{)}^2}{{\mathrm{2m}}^6}$ ..................................................

1.4 $\frac{4({\mathrm{2m}}^2{)}^5}{2(m^2{)}^2}$ ..................................................

1.5 $\frac{{\mathrm{8a}}^2(a^2{)}^2}{{\mathrm{8a}}^2}$ ..................................................

1.6 $\frac{\text{25}{a}^2{b}^3{c}^4\text{.}4{\text{ab}}^3{c}^2}{\text{15}{a}^3{b}^4{c}^5}$ ...........................................

2. Remember: $\frac{1}{3}b(\mathrm{9a})$ = $\frac{1\times b}{3}\times \frac{\mathrm{9a}}{1}$ = $\frac{b\times \mathrm{9a}}{3}=\frac{9\text{ab}}{3}$ = 3 ab

Therefore: $\frac{1}{3}$ means: x 1 ÷ 3

Now try to simplify the following: ¹ / ₃ ( 4 a - 6 b )

2.1 Write each of the following in simplified form.

2.1.1: $\frac{1}{5}$ x a ..................................................

2.1.2: $\frac{1}{5}$ (2 a ² - 15) ..................................................

2.1.3: (2 a - 8 b + 12 c ) ÷ 2 ..................................................

2.1.4: $\frac{{\mathrm{6a}}^2{b}^2{c}^3\text{- 15}{a}^4{b}^6{c}^7+\text{27}{b}^9{c}^{\text{10}}}{{\mathrm{3a}}^2{b}^4{c}^3}$

2.1.5: $\frac{{\mathrm{7m}}^2{\text{pq}}^9\text{- 49}{m}^6{n}^7\text{- 35}{p}^6{q}^{\text{12}}}{-7{\text{mn}}^3{q}^4}$

HOMEWORK ASSIGNMENT 1

1. Simplify:

1.1 $\frac{\text{- 56}{p}^7{q}^7}{\text{-8}{\text{mn}}^3{q}^4}$

1.2 $\frac{{\mathrm{3a}}^2{\text{bc}}^4\text{- 36}{a}^4{b}^7+\text{24}{a}^3{b}^2}{\text{-3}{\text{ab}}^2{c}^2}$

1.3 ½ (5 a ² - 25 b )

1.4 $\frac{(a^2{b}^2{)}^3\text{.}({\text{ab}}^2{)}^4}{a^2{b}^3}$

1.5 $\frac{3(4{\text{kp}}^4{)}^2}{{\mathrm{2k}}^3{p}^2}$

2. If P = 3 ab ² + 6 a ² and Q = 2 ab , calculate:

2.1 2 P - 3 Q

2.2 $\frac{P}{Q}$

2.3 $\frac{P+Q}{\mathrm{2Q}}$

3. Supposing that 5 a ³ b ² books cost (-5 ab + 15 a ⁴ b ⁷ ) rands, calculate the price of one book.

Assessment

 good  average  not so good

Tutorial 2: (Algebra)

Total: 70

Question 1

A. Indicate whether the following statements are TRUE or FALSE and improve the wrong statements.

1. The base of 2 $x$ ³ is 2 $x$ .

2. The number of terms in the expression are THREE:3(5 a + 2) + 5 b - 6

3. -10 ½<-10,499

4. -2² = -4

5. The first prime number is 1.