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

Question 59

We need to check if ( frac{8}{18} - frac{8}{15} = frac{8}{3} ).

1. Find a common denominator for ( frac{8}{18} ) and ( frac{8}{15} ).

   ( ext{LCM}(18, 15) = 90 ).

2. Rewrite each fraction with denominator 90.

   ( frac{8}{18} = frac{8 imes 5}{18 imes 5} = frac{40}{90} )

   ( frac{8}{15} = frac{8 imes 6}{15 imes 6} = frac{48}{90} )

3. Subtract the numerators (same denominator).

   ( frac{40}{90} - frac{48}{90} = frac{40 - 48}{90} = frac{-8}{90} )

4. Simplify the result.

   ( frac{-8}{90} = frac{-4}{45} ) (divide top and bottom by 2)

5. Compare with the right side ( frac{8}{3} ).

   Write ( frac{8}{3} ) with denominator 45: ( frac{8}{3} = frac{8 imes 15}{3 imes 15} = frac{120}{45} )

   ( frac{-4}{45} eq frac{120}{45} )

6. Conclusion: The statement is false because

   ( frac{8}{18} - frac{8}{15} = frac{-4}{45} ), not ( frac{8}{3} ).