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

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

Answer 2

`\boxed{\bf \sf number : \ (4)/(5) }`

Step-by-step explanation:

Let the number be n

According to students Condition:

`\rightarrow \sf (3)/(2) \ x \ n \quad = \quad (3n)/(2)`

What He actually Did:

`\rightarrow \sf n / (3)/(2) \quad = \quad n \ x \ (2)/(3) \quad = \quad (2n)/(3)`

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

`\rightarrow \sf (3n)/(2) - (2n)/(3) = (2)/(3)`

make the denominator's same

`\rightarrow \sf (3(3n))/(6) - (2(2n))/(6) = (2)/(3)`

multiply the integers

`\rightarrow \sf (9n)/(6) - (4n)/(6) = (2)/(3)`

Join the fractions

`\rightarrow \sf (9n-4n)/(6) = (2)/(3)`

Subtract integers

`\rightarrow \sf (5n)/(6) = (2)/(3)`

Cross multiply

`\rightarrow \sf n = (6 \ * \ 2)/(5 \ * \ 3) \quad = \quad (4)/(5)`