Lesson 9, Topic 1
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# Simple Equations Involving Fractions

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To solve simple equations containing fractions, first eliminate the fractions by multiplying each term in the equation by the LCM of the denominator.

i. $$\frac{x}{12} = \scriptsize 5$$

$$\frac{x}{12}\scriptsize \: \times \: 12 = 5 \: \times \: 12$$

$$\scriptsize x = 12 \: \times \: 5 \\ \scriptsize = 60$$

ii. $$\frac{x}{9} = \frac{4}{3}$$

Cross multiply

$$\frac{x\: \searrow}{9 \: \nearrow} = \frac{ \swarrow \: 4}{\nwarrow \: 3 }$$

$$\scriptsize 3 \: \times \: x = 9 \: \times \: 4$$

$$\scriptsize 3x = 36$$

Divide by 3

$$\frac{3x}{3} = \frac{36}{3}$$

$$\frac{\not{3}x}{\not{3}} = \frac{36}{3}$$

x = 12

iii. $$\frac{y \: – \: 5}{4} = \scriptsize 8$$

Multiply through by 4

$$\scriptsize 4 \: \times \: \normalsize \frac{y \: – \: 5}{4} = \scriptsize 4 \: \times \: 8$$

$$\scriptsize y \: – \: 5 = 32$$

$$\scriptsize y \: – \: 5 \: + \: 5 = 32 \: + \: 5$$

$$\scriptsize y = 37$$

iv. $$\scriptsize 2x \: – \: \normalsize \frac{x}{8} = \scriptsize 12 \frac{1}{2}$$

$$\frac{2x}{1} \: – \: \frac{x}{8}= \frac{25}{2}$$

Take the L.C.M

$$\frac{8(2x)\: – \: 1(x)}{8} = \frac{25}{2}$$

$$\frac{16x\: – \: x}{8} = \frac{25}{2}$$

$$\frac{15x}{8} = \frac{25}{2}$$

$$\scriptsize 15x \: \times \: 2 =25 \: \times \: 8$$

$$\scriptsize 30x =200$$

x = $$\frac{200}{30}$$

x = $$\scriptsize 6 \frac{2}{3} \: or \: 6.67$$

v. $$\frac{5x \: – \: 1}{4} = \frac{2x \: – \: 1}{2}$$

Cross multiply

$$\scriptsize 2(5x \: – \: 1) = 4(2x \: – \: 1)$$

$$\scriptsize 10x \: – \: 2 = 8x \: – \: 4$$

Take like terms

$$\scriptsize 10x \: – \: 8x = -4 \: + \: 2$$

$$\scriptsize 2x = -2$$

Divide both sides by 2

$$\frac {2x}{2} =\frac{ -2}{2}$$

x = -1

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