Question

a student was asked to multiply a number by 3/2. instead he divided the number by 3/2 and obtained a number smaller by 2/3, the number is:

Answer 1

Answer:

$\boxed{\bf \sf number : \ \frac{4}{5} }$

Explanation:

Let the number be n

According to students Condition:

$\rightarrow \sf \dfrac{3}{2} \ x \ n \quad = \quad \dfrac{3n}{2}$

What He actually Did:

$\rightarrow \sf n \div \dfrac{3}{2} \quad = \quad n \ x \ \dfrac{2}{3} \quad = \quad \dfrac{2n}{3}$

He got a smaller number by 2/3, so:

$\rightarrow \sf \dfrac{3n}{2} - \dfrac{2n}{3} = \dfrac{2}{3}$

make the denominator's same

$\rightarrow \sf \dfrac{3(3n)}{6} - \dfrac{2(2n)}{6} = \dfrac{2}{3}$

multiply the integers

$\rightarrow \sf \dfrac{9n}{6} - \dfrac{4n}{6} = \dfrac{2}{3}$

Join the fractions

$\rightarrow \sf \dfrac{9n-4n}{6} = \dfrac{2}{3}$

Subtract integers

$\rightarrow \sf \dfrac{5n}{6} = \dfrac{2}{3}$

Cross multiply

$\rightarrow \sf n = \dfrac{6 \ * \ 2}{5 \ * \ 3} \quad = \quad \dfrac{4}{5}$

Answer 2

Lets see

the number be x

The expression is

• 3x/2-2x/3=2/3
• 9x-4x)6=2/3
• 5x)6=2/3
• 15x=12
• x=12/15=4/5