15 m : 40 m = 35 m : 65 m
Write each ratio as a fraction.
( rac{15}{40} ) and ( rac{35}{65} )
Simplify both fractions to lowest terms.
For ( rac{15}{40} ):
( gcd(15,40) = 5 )
( rac{15 div 5}{40 div 5} = rac{3}{8} )
For ( rac{35}{65} ):
( gcd(35,65) = 5 )
( rac{35 div 5}{65 div 5} = rac{7}{13} )
Compare the simplified fractions using cross-multiplication.
Multiply diagonally:
( 3 imes 13 = 39 )
( 8 imes 7 = 56 )
Since ( 39 eq 56 ), the fractions are not equal.
Conclusion.
( 15 ext{ m} : 40 ext{ m} eq 35 ext{ m} : 65 ext{ m} )
Answer: false.
Optional check (decimals):
( rac{3}{8} = 0.375 )
( rac{7}{13} approx 0.538 )
These are different, so the ratios are not equal.