Compare the following fractions and justify your answers : Class 6

Compare the following fractions and justify your answers : Class 6

Question 1.

Compare the following fractions and justify your answers : Class 6

Solution:

(a) $\frac{8}{3}=\frac{16}{6}$ and $\frac{5}{2}=\frac{15}{6}$.

Now, $\frac{16}{6}>\frac{15}{6}$. Hence, $\frac{8}{3}>\frac{5}{2}$.

(b) $\frac{4}{9}=\frac{4 \times 7}{9 \times 7}=\frac{28}{63}$ and $\frac{3}{7}=\frac{3 \times 9}{7 \times 9}=\frac{27}{63}$.

Now, $\frac{28}{63}>\frac{27}{63}$. So, $\frac{4}{9}>\frac{3}{7}$.

(c) $\frac{7}{10}=\frac{7 \times 7}{10 \times 7}=\frac{49}{70}$ and $\frac{9}{14}=\frac{9 \times 5}{14 \times 5}=\frac{45}{70}$.

(70 is the first common multiple of 10 and 14)

Now, $\frac{49}{70}>\frac{45}{70}$. So, $\frac{7}{10}>\frac{9}{14}$.

(d) $\frac{12}{5}>\frac{8}{5}$, since $12>8$.

(e) $\frac{9}{4}=\frac{9}{4}$ and $\frac{5}{2}=\frac{10}{4}$.

Now, $\frac{9}{4}<\frac{10}{4}$. So, $\frac{9}{4}<\frac{5}{2}$.