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 \(\frac{3}4\)