Question

The given equation represents the sum of the fractions represented on the line plot:


$Sum=(3\times \frac{1}{8})+(3\times \frac{1}{4})+(1\times \frac{1}{2})$

Choose the line plot whose fractions add up to give the same sum:

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

Answer 1

The correct option is D Plot D

The sum of the fractions of the given plot is:

$Sum=(3\times \frac{1}{8})+(3\times \frac{1}{4})+(1\times \frac{1}{2})$

Now, this sum can be expressed as:

$Sum=(3\times \frac{1}{8})+(3\times \frac{1}{4})+(1\times \frac{1}{2})$

$=(\frac{1}{8}+\frac{1}{8}+\frac{1}{8})+(\frac{1}{4}+\frac{1}{4}+\frac{1}{4})+\frac{1}{2}$

$=\frac{1}{8}+(\frac{1}{8}+\frac{1}{8})+\frac{1}{4}+(\frac{1}{4}+\frac{1}{4})+\frac{1}{2}$

$=\frac{1}{8}+\left(\frac{2}{8}\right)+\frac{1}{4}+\left(\frac{2}{4}\right)+\frac{1}{2}$

$\text{Now,}\frac{2}{8}=\frac{1}{4}$

$\text{Also,}\frac{2}{4}=\frac{1}{2}$

$⟹Sum=\frac{1}{8}+\left(\frac{2}{8}\right)+\frac{1}{4}+\left(\frac{2}{4}\right)+\frac{1}{2}$

$=\frac{1}{8}+\left(\frac{1}{4}\right)+\frac{1}{4}+\left(\frac{1}{2}\right)+\frac{1}{2}$

$=\frac{1}{8}+(\frac{1}{4}+\frac{1}{4})+\frac{1}{2}+\frac{1}{2}$

$=\frac{1}{8}+\left(\frac{2}{4}\right)+\frac{1}{2}+\frac{1}{2}$

$=\frac{1}{8}+\left(\frac{1}{2}\right)+\frac{1}{2}+\frac{1}{2}$

Rewriting this, we find:

$Sum=(1\times \frac{1}{8})+(0\times \frac{1}{4})+(3\times \frac{1}{2})$

Plotting the number of each type of fraction on a line plot, we get:


Hence, the fractions represented in plot D add up to give the sum given in the question.