Question

James plots the six steps he takes from his bedroom door to his bed as a line plot. Later, James decides to walk the same distance in only 5 steps with each step measuring either half a metre or an eighth of a metre. If so, choose the correct line plot that represents James' walk.

• A. Plot A
• B. Plot D
• C. Plot B
• D. Plot C

Answer 1

The correct option is D Plot C

$Giveninitiallineplot:$


$\text{We can tabulate the data from the initial}\text{line plot as:}$

Length of the step (m)	Number of steps	Total distance covered (m)
$\frac{1}{2}$	$2$	$\frac{1}{2}+\frac{1}{2}=\frac{2}{2}$
$\frac{1}{4}$	$2$	$\frac{1}{4}+\frac{1}{4}=\frac{2}{4}$
$\frac{1}{8}$	$2$	$\frac{1}{8}+\frac{1}{8}=\frac{2}{8}$
$\text{Total}$	$6$	$\frac{2}{2}+\frac{2}{4}+\frac{2}{8}$

$\text{Now,}\frac{2}{2}=\frac{2\times 4}{2\times 4}=\frac{8}{8}⟹\frac{8}{8}\text{is an equivalent fraction of}\frac{2}{2}$

$\text{Similarly,}\frac{2}{4}=\frac{2\times 2}{4\times 2}=\frac{4}{8}⟹\frac{4}{8}\text{is an equivalent fraction of}\frac{2}{4}$

$\therefore \text{The total distance covered initially can be}$ $\text{calculated as:}$

$\frac{2}{2}+\frac{2}{4}+\frac{2}{8}=\frac{8}{8}+\frac{4}{8}+\frac{2}{8}=\frac{14}{8}\text{m}$

$\text{Now, to cover the distance in 5 steps,}$

$\frac{14}{8}=\frac{4}{8}+\frac{4}{8}+\frac{4}{8}+\frac{1}{8}+\frac{1}{8}$

$\text{Also,}$

$\frac{4}{8}=\frac{4÷4}{8÷4}=\frac{1}{2}$

$⟹\frac{4}{8}\text{is an equivalent fraction of}\frac{1}{2}$

$\therefore \text{The total distance covered can be}$ $\text{written as:}$

$\frac{14}{8}\text{m}=\frac{1}{2}\text{m}+\frac{1}{2}\text{m}+\frac{1}{2}\text{m}+\frac{1}{8}\text{m}+\frac{1}{8}\text{m}$

$⟹\frac{14}{8}\text{m can be covered in 5 steps}\text{where 3 steps measure}\frac{1}{2}\text{m each,}\text{while the rest 2 steps measure}\frac{1}{8}\text{m each.}$

$\text{Tabulating this data, we get:}$

$\text{Length of the step (m)}$	$\text{Number of steps}$
$\frac{1}{2}$	$3$
$\frac{1}{8}$	$2$

$\text{Plotting the data on a line plot, we get:}$


$\therefore \text{The correct line plot that represents}$ $\text{James' walk is plot C.}$