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# 1.If you subtract $$\frac { 1 }{ 2 }$$ from a number and multiply the result by $$\frac { 1 }{ 2 }$$, you get $$\frac { 1 }{ 8 }$$. What is the number?

Let the number be x
Condition 1: $$x-\frac{1}2$$

Condition 2: $$(x-\frac{1}2) ×\frac{1}2$$

Condition 3: $$x-\frac{1}2) ×\frac{1}2 =\frac{1}8$$

$$\Rightarrow (x-\frac{1}2) ×\frac{1}2 × 8=\frac{1}8×8\quad$$[multiplying both the sides by 8]

$$\Rightarrow (x-\frac{1}2) ×4=1$$

$$\Rightarrow 4x-\frac{1}2 ×4=1\quad$$[opening the brackets]

$$\Rightarrow 4x-2=1$$

$$\Rightarrow 4x-2+2=1+2 \quad$$[adding 2 to both the sided]
$$\Rightarrow 4x=3$$

$$\Rightarrow 4x÷4= 3÷4\quad$$[dividing both the sides by 4]

$$\Rightarrow x=\frac{3}4$$

Thus, the required number is $$\frac{3}4$$