NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - Problems and Solutions
Question 122

Question. 122

What is wrong in the following additions?

Q122 figures

Answer:

(a) Denominators have been added wrongly; the correct sum is \(8\tfrac{2}{4}+4\tfrac{1}{4}=12\tfrac{3}{4}\), not \(12\tfrac{3}{8}\).

(b) Denominators must not be added; the correct sum is \(6\tfrac{1}{2}+2\tfrac{1}{4}=8\tfrac{3}{4}\), not \(8\tfrac{1}{3}\).

Detailed Answer with Explanation:

Key idea: When adding fractions, do not add denominators. Make the denominators the same, then add only the numerators.

(a) (8 frac{2}{4}+4 frac{1}{4})

  1. Check denominators: (4) and (4). They are already the same.
  2. Add whole numbers: (8+4=12).
  3. Add fractions: ( frac{2}{4}+ frac{1}{4}= frac{3}{4}).
  4. Combine the results: (12+ frac{3}{4}=12 frac{3}{4}).

Error in the picture: Denominators were added to get ( frac{3}{8}). That is wrong. The correct answer is (12 frac{3}{4}).

(b) (6 frac{1}{2}+2 frac{1}{4})

  1. Denominators are (2) and (4). Make them the same.
  2. Convert ( frac{1}{2}) to quarters: multiply top and bottom by (2).
    ( frac{1}{2}= frac{2}{4}).
  3. Now add (6 frac{2}{4}+2 frac{1}{4}).
  4. Add whole numbers: (6+2=8).
  5. Add fractions: ( frac{2}{4}+ frac{1}{4}= frac{3}{4}).
  6. Combine the results: (8+ frac{3}{4}=8 frac{3}{4}).

Error in the picture: Denominators were added to get ( frac{1}{3}). That is wrong. The correct answer is (8 frac{3}{4}).

Remember: Same denominators → add numerators. Different denominators → first make them the same, then add.

Open NCERT PDF