Question

Find 7 rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$.

• A. $\frac{31}{90},\frac{16}{45},\frac{11}{30},\frac{17}{45},\frac{7}{18},\frac{2}{5},\frac{37}{90}$
• B. $\frac{30}{90},\frac{16}{45},\frac{11}{30},\frac{17}{45},\frac{7}{18},\frac{2}{5},\frac{37}{90}$
• C. $\frac{31}{90},\frac{16}{45},\frac{29}{30},\frac{17}{45},\frac{7}{18},\frac{2}{5},\frac{37}{90}$
• D. $\frac{31}{90},\frac{32}{45},\frac{11}{30},\frac{17}{45},\frac{7}{18},\frac{2}{5},\frac{37}{90}$

Answer 1

The correct option is A $\frac{31}{90},\frac{16}{45},\frac{11}{30},\frac{17}{45},\frac{7}{18},\frac{2}{5},\frac{37}{90}$

We can write $\frac{1}{3}=\frac{1\times 30}{3\times 30}=\frac{30}{90}$

$\frac{1}{2}=\frac{1\times 45}{2\times 45}=\frac{45}{90}$

$\therefore \frac{30}{90}<\frac{31}{90}.....<\frac{35}{90}......\frac{45}{90}$
Thus, the required rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$ are
$\frac{31}{90},\frac{32}{90},\frac{33}{90},\frac{34}{90},\frac{35}{90},\frac{36}{90},\frac{37}{90}$

Simplifying them we have,
$\frac{31}{90},\frac{16}{45},\frac{11}{30},\frac{17}{45},\frac{7}{18},\frac{2}{5},\frac{37}{90}$