NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 7: Algebra - True or False Questions

Question 53

Why the given statement is translated wrongly

Statement: “One third of a number added to itself gives 8.”

1. Let the number be ( x ).
2. “One third of a number” means
   (dfrac{1}{3} imes x)
   which we write as
   (dfrac{x}{3}).
3. “Added to itself” means we add the number ( x ) to (dfrac{x}{3}):
   (dfrac{x}{3} + x).
4. “Gives 8” means the result equals 8:
   (dfrac{x}{3} + x = 8).

So, the correct equation is:
(dfrac{x}{3} + x = 8).

The given equation in the question was:
(dfrac{x}{3} + 8 = x),
which places (8) on the left side and (x) on the right side. That does not match the words of the statement, so it is false.

(Optional check) Solve the correct equation to verify:

1. Add the like terms:
   (dfrac{x}{3} + x = dfrac{x}{3} + dfrac{3x}{3} = dfrac{4x}{3}).
2. Set equal to 8:
   (dfrac{4x}{3} = 8).
3. Multiply both sides by 3:
   (4x = 24).
4. Divide by 4:
   (x = 6).

Check: (dfrac{6}{3} + 6 = 2 + 6 = 8) Correct.