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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:

User Scorpil
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2 Answers

11 votes
11 votes

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
User Sasha Kozachuk
by
3.1k points
6 votes
6 votes

Answer:


\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)

User Lee Harold
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