NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - True or False Questions
Question 58

Question. 58

\(\tfrac{25}{19}+\tfrac{6}{19}=\tfrac{31}{38}\).

Answer:

false

Detailed Answer with Explanation:

  1. Look at the left side (LHS): ( frac{25}{19} + frac{6}{19} ).
  2. Both fractions have the same denominator (19).
    Rule: When denominators are the same, add the numerators and keep the denominator.
  3. Add the numerators: ( 25 + 6 = 31 ).
  4. So, ( frac{25}{19} + frac{6}{19} = frac{31}{19} ).
  5. The right side (RHS) is ( frac{31}{38} ).
  6. To compare, write ( frac{31}{19} ) with denominator (38): multiply top and bottom by (2).
    ( frac{31}{19} = frac{31 imes 2}{19 imes 2} = frac{62}{38} ).
  7. Now compare: ( frac{62}{38} eq frac{31}{38} ).

Therefore, the statement ( frac{25}{19} + frac{6}{19} = frac{31}{38} ) is false. The correct sum is ( frac{31}{19} ) (which is ( 1 frac{12}{19} ) as a mixed number).

Open NCERT PDF