Lesson 4, Topic 2
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# Simplifying Fractions

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To simplify a fraction means to reduce it to its simplest form

### Example 3

Simplify each of the following fractions

(a) $$\frac{2b}{2a}$$

(b) $$\frac{16a^3}{4a^2}$$

(c) $$\frac{x^2}{x^4}$$

(d) $$\frac{8e^3f}{10ef^2}$$

(e) $$\frac{10y}{15z}$$

Solution

(a) $$\frac{2b}{2a} \\ = \frac{2 \: \times \: b }{2\: \times \: a}\\ = \frac{\not{2} \: \times \: b }{\not{2} \: \times \: a} \\ = \frac{b}{a}$$

(b) $$\frac{16a^3}{4a^2} \\ =\frac{16\: \times \:a \: \times \:a\: \times \:a}{4\: \times \: a\: \times \:a}\\ =\frac{16\: \times \:a \: \times \: \not{a}\: \times \: \not{a}}{4\: \times \: \not{a}\: \times \:\not{a}} \\ = \frac{16\: \times \:a }{4} \\ = \scriptsize 4 \: \times \: a \\ = \scriptsize 4a$$

(c) $$\frac{x^2}{x^4} \\ = \frac{x \: \times \: x}{x \: \times \: x \: \times \: x \: \times \: x} \\ = \frac{\not{x} \: \times \: \not{x}}{\not{x} \: \times \: \not{x} \: \times \: x \: \times \: x} \\ = \frac{1}{x \: \times \: x} \\ = \frac{1}{x^2}$$

(d) $$\frac{8e^3f}{10ef^2} \\ = \frac{8\: \times \:e\: \times \:e\: \times \:e\: \times \:f}{10\: \times \:e\: \times \:f\: \times \:f} \\ = \frac{8\: \times \:e\: \times \:e\: \times \:\not{e} \: \times \:\not{f}}{10\: \times \:\not{e}\: \times \:f\: \times \: \not{f}} \\ = \frac{8\: \times \:e\: \times \:e}{10\: \times \: f } \\ = \frac{ \not{8}^{4} \: \times \:e\: \times \:e}{\not{10}^{5}\: \times \: f } \\ = \frac{4\: \times \:e\: \times \:e}{5\: \times \: f } \\ = \frac{4e^2}{5f}$$

(e) $$\frac{10y}{15z} \\ = \frac{10\: \times \: y}{15\: \times \:z} \\ = \frac{2\: \times \: y}{3\: \times \:z} \\ = \frac{2y}{3z}$$

Evaluation

Simplify the following fraction

(a) $$\frac{2xy}{yz}$$

(b) $$\frac{4a}{7a}$$

(c) $$\frac{12ab^2}{18a^2b^2}$$

(d) $$\frac{-16}{2b}$$

(e) $$\frac{-15x^2y}{3x^3}$$

(f) $$\frac{9mn^2}{3m^2}$$

(a) $$\frac{2x}{z}$$

(b) $$\frac{4}{7}$$

(c) $$\frac{2}{3a}$$

(d) $$\frac{-8}{b}$$

(e) $$\frac{-5y}{x}$$

(f) $$\frac{3n^2}{3m}$$

error: