Given
The ratios,
A. 1 : 6 and 3 : 18
B. 2 : 14 and 3 : 42
C. 12 : 6 and 2 : 1
D. 3 : 11 and 6 : 22
To find the ratios which are not equal.
Explanation:
It is given that,
A. 1 : 6 and 3 : 18
That implies,
[tex]\begin{gathered} \frac{3}{18}=\frac{3}{6\times3} \\ =\frac{1}{6} \end{gathered}[/tex]Hence, the ratios 1 : 6 and 3 : 18 are equal.
B. 2 : 14 and 3 : 42
That implies,
[tex]\begin{gathered} \frac{2}{14}=\frac{2}{2\times7} \\ =\frac{1}{7} \\ \frac{3}{42}=\frac{3}{3\times2\times7} \\ =\frac{1}{14} \\ \Rightarrow\frac{2}{14}\ne\frac{3}{42} \end{gathered}[/tex]Hence, the ratios 2 : 14 and 3 : 42 are not equal.
C. 12 : 6 and 2 : 1
That implies,
[tex]\begin{gathered} \frac{12}{6}=\frac{2\times6}{6} \\ =\frac{2}{1} \end{gathered}[/tex]Hence, the ratios C. 12 : 6 and 2 : 1 are equal.
D. 3 : 11 and 6 : 22
That implies,
[tex]\begin{gathered} \frac{6}{22}=\frac{2\times3}{2\times11} \\ =\frac{3}{11} \end{gathered}[/tex]Hence, the ratios D. 3 : 11 and 6 : 22 are equal.
Thus, the ratios B. 2 : 14 and 3 : 42 are not equal.
