\(3:33 = 33:333\)
To check if two ratios are equal, change them into fractions and compare.
Given statement: (3:33 = 33:333)
As fractions: (dfrac{3}{33}) and (dfrac{33}{333})
Simplify the first fraction:
(dfrac{3}{33} = dfrac{3 div 3}{33 div 3} = dfrac{1}{11})
Simplify the second fraction:
Both 33 and 333 are divisible by (3).
(dfrac{33}{333} = dfrac{33 div 3}{333 div 3} = dfrac{11}{111})
(No further common factor, so it stays (dfrac{11}{111}).)
Compare the simplified forms:
(dfrac{1}{11} = 0.090909ldots)
(dfrac{11}{111} = 0.099099ldots)
These decimals are different, so the ratios are not equal.
Quick cross-multiplication check (optional):
Compare (3 imes 333) and (33 imes 33).
(3 imes 333 = 999)
(33 imes 33 = 1089)
Since (999 e 1089), the ratios are not equal.