Question

(a) In the figure given below, normally in two jumps frog covers the distance of 9m. One day on seeing the snake frog jumped $\frac{1}{5}$ times more than his normal jump and again he jumped with full strength and covered $\frac{1}{2}$ times more distance than he normally covers in the second jump. Find the distance covered by frog in the second jump and in total.

(b) Are the statements below correct?

(i) The rational numbers $\frac{-21}{5}$ and $\frac{7}{-31}$ are on the opposite sides of 0 on the number line.

(ii) The rational number $\frac{-3}{-5}$ is on the right of $\frac{-4}{7}$ on the number line.

[4 MARKS]

Answer 1

Each part: 2 Marks

(a) In normal jump frog covers 5m in first jump but this time his jump covered $=5+(5\times \frac{1}{5})=6m$

In the second jump it covered $=4+(4\times \frac{1}{2})=6m$.

So, distance covered in second jump = 6m.

Total distance covered by frog = 6m + 6m = 12m


(b) (i) The statement is false as $\frac{-21}{5}$ and $\frac{7}{-31}$ both are negative numbers and lie to the left side of 0 on the number line i.e. they are at the same side to that of 0 which is left.

(ii) This statement is true as the number $\frac{-3}{-5}$ is actually positive $\frac{3}{5}$ and $\frac{-4}{7}$ is negative. Therefore, $\frac{3}{5}$ is is on the right of $\frac{-4}{7}$ on the number line.