Question

If you subtract 1/2 from a noumber and multiply the result by 1/2, you get 1/8. What is the number?​

Answer 1

Given :

• We need to subtract $\tt\:\frac{1}{2}$ from a number.

• The value which we would get after subtraction needs to be multiplied by $\tt\:\frac{1}{2}$

• The result after subtraction and multiplication is given to be as $\tt\:\frac{1}{8}$

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To find :

• The number which when subtracted and multiplied by $\tt\:\frac{1}{2}$ gives $\tt\:\frac{1}{8}$ as the final result

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Concept :

In order to do this question we would frame an equation following the criterias given in the question.

We would assume the required number as any variable , then after we would subtract and multiply the variable by 1/2 . After doing so whatever would be the result we would equate it with 1/8 . Finally solving this equation we would get our required number.

Hope am clear let's solve :D~

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Assumption :

Let the required number be x.

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Solution :

According to the question :

❒ Firstly, subtracting $\tt\:\frac{1}{2}$ from x -

$\tt\therefore\:x-\frac{1}{2}$

❒ Secondly , multiplying the result we got after subtraction by $\tt\:\frac{1}{2}$ -

$\tt\therefore\:x-\frac{1}{2} \times \frac{1}{2}$

❒ Now we are said that after subtraction and multiplication the result would be $\tt\:\frac{1}{8}$ -

$\tt\:Equation:\:x-\frac{1}{2} \times \frac{1}{2}=\frac{1}{8}$

Proceeding with multiplication at LHS

$\tt:\implies\:x-\frac{1}{4}=\frac{1}{8}$

LCM of 1 and 4 = 4 in LHS

$\tt:\implies\:\frac{(4 \times x) +(1 \times 1)}{4}=\frac{1}{8}$

$\tt:\implies\:\frac{4x+1}{4}=\frac{1}{8}$

Cross multiplying

$\tt:\implies\:8(4x-1)=1 \times 4$

$\tt:\implies\:32x-8=4$

Transposing +4 from RHS to LHS it becomes -4

$\tt:\implies\:32x-8-4=0$

$\tt:\implies\:32x-12=0$

Transposing -12 from LHS to RHS it becomes +12

$\tt:\implies\:32x=12$

Transposing 32 from LHS to RHS it goes to the denominator

$\tt:\implies\:x=\frac{12}{32}$

Reducing the fraction to the lower terms

$\tt:\implies\:x=\cancel{\frac{12}{32}}$

$\tt:\implies\:x=\cancel{\frac{6}{16}}$

$\small{\underline{\boxed{\mathrm{:\implies\:x~=~\frac{3}{8}}}}}$ ★

$\tt\maltese$ So we got the number as $\large{\mathfrak\purple{\frac{3}{8}}}$

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Verification :

Plugging the value of x as $\tt\:\frac{3}{8}$ in the equation we had framed earlier :

$\tt\:Equation:\:x-\frac{1}{2} \times \frac{1}{2}=\frac{1}{8}$

$\tt\leadsto\:\frac{3}{8}-\frac{1}{2} \times \frac{1}{2}=\frac{1}{8}$

$\tt\leadsto\:\frac{3}{8}-\frac{1}{4}=\frac{1}{8}$

$\tt\leadsto\:\frac{(1 \times 3) - (2 \times 1)}{8}=\frac{1}{8}$

$\tt\leadsto\:\frac{3-2}{8}=\frac{1}{8}$

$\tt\leadsto\:\frac{1}{8}=\frac{1}{8}$

$\tt\leadsto\:LHS=RHS$

Hence Verified !~

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