Question

Which fraction is greater than the fraction 3:8,
a. 1:4
b. 7:16
c. 1:8
d. 3 :16

Answer 1

Look, that:

$\dfrac{1}{4} = \dfrac{2}{8} \\ \\ \dfrac{7}{16}= \dfrac{3.5}{8} \\ \\ \dfrac{1}{8} \\ \\ \dfrac{3}{16}=\dfrac{1.5}{8}$

(in second and fourth fractions just divide nominator and denominator by 2). Greater than 3/8  is  this fraction, which has nominator greater than 3.  It is  3.5/8.  So  7:16  - answer b)

Answer 2

$\frac{3}{8} \\ \frac{1}{4}=\frac{1 \times 2}{4 \times 2}=\frac{2}{8} \\ 3 \ \textgreater \ 2 \Rightarrow \frac{3}{8} \ \textgreater \ \frac{2}{8} \Rightarrow \frac{3}{8}\ \textgreater \ \frac{1}{4} \\ \hbox{not greater} \\ \\ \frac{3}{8}=\frac{3 \times 2}{8 \times 2}=\frac{6}{16} \\ \frac{7}{16} \\ 6\ \textless \ 7 \Rightarrow \frac{6}{16} \ \textless \ \frac{7}{16} \Rightarrow \frac{3}{8} \ \textless \ \frac{7}{16} \\ \hbox{greater}$

$\frac{3}{8} \\ \frac{1}{8} \\ 3\ \textgreater \ 1 \Rightarrow \frac{3}{8} \ \textgreater \ \frac{1}{8} \\ \hbox{not greater} \\ \\ \frac{3}{8} =\frac{3 \times 2}{8 \times 2}=\frac{6}{16} \\ \frac{3}{16} \\ 6\ \textgreater \ 3 \Rightarrow \frac{6}{16} \ \textgreater \ \frac{3}{16} \Rightarrow \frac{3}{8} \ \textgreater \ \frac{3}{16} \\ \hbox{not greater}$

The answer is B.