Question

Find the quotient in each of the following
5m 8dm 4cm 8mm $\div $ 12

Answer 1

Hint: We solve this question by first taking the given value and then we convert the whole value in a single unit by first converting the value 8dm into m using the formula $1m=10dm$ and then we convert 4cm into m, using the formula $1m=100cm$ and then we convert 8mm to “m” using the formula $1m=1000mm$. Then we add all the obtained values and find the whole value in m. Then we divide it by 12 and find the quotient.

Complete step-by-step solution:
Here we need to find the quotient when 5m 8dm 4cm 8mm is divided by 12.
As we see the dividend, 5m 8dm 4cm 8mm is not in a single unit.
So, let us convert it into a single unit.
So, let us convert the complete 5m 8dm 4cm 8mm into meters.
First, let us consider the value of 8dm.
Now let us consider the formula between meters and dm.
$1 meter = 10 dm.$
As we need to convert the dm into m, we can convert the above formula as,
$1 dm = 0.1 m$
Using it, we can convert 8dm as
\[\begin{align}
  & \Rightarrow 8dm=8\times 0.1m \\
 & \Rightarrow 8dm=0.8m.............\left( 1 \right) \\
\end{align}\]
First let us consider the value 4cm.
Now let us consider the formula between meters and cm.
$1 meter = 100 cm.$
As we need to convert the cm into m, we can convert the above formula as,
$1 cm = 0.01 m$
Using it, we can convert 4cm as
\[\begin{align}
  & \Rightarrow 4cm=4\times 0.01m \\
 & \Rightarrow 4cm=0.04m.............\left( 2 \right) \\
\end{align}\]
First let us consider the value 8mm.
Now let us consider the formula between meters and dm.
$1 meter = 1000 mm.$
As we need to convert the mm into m, we can convert the above formula as,
$1 mm = 0.001 m$
Using it, we can convert 8mm as
\[\begin{align}
  & \Rightarrow 8mm=8\times 0.001m \\
 & \Rightarrow 8mm=0.008m.............\left( 3 \right) \\
\end{align}\]
Now using the equations (1), (2) and (3), we can write 5m 8dm 4cm 8mm as,
$\begin{align}
  & \Rightarrow 5m\text{ }8dm\text{ }4cm\text{ }8mm=\left( 5+0.8+0.04+0.008 \right)m \\
 & \Rightarrow 5m\text{ }8dm\text{ }4cm\text{ }8mm=5.848m \\
\end{align}$
Now, let us divide it with 12.
$12\overset{0.4873}{\overline{\left){\begin{align}
  & 5.848 \\
 & \underline{48\ \ \ \ \ \ } \\
 & 104 \\
 & \underline{\text{ }96\text{ }} \\
 & \text{ }88 \\
 & \underline{\text{ }84\text{ }} \\
 & \text{ 40} \\
 & \underline{\text{ 36}} \\
 & \text{ 4} \\
\end{align}}\right.}}$
Hence quotient is 0.4873.
We can round it off to 0.49.
Hence answer is 0.49.

Note: There is a possibility of one making a mistake as, after converting all the given units in the question into a single unit. One might multiply them as,
$\Rightarrow 5m\text{ }8dm\text{ }4cm\text{ }8mm=\left( 5\times 0.8\times 0.04\times 0.008 \right)m=0.00128m$, But it is wrong. Here 5m 8dm 4cm 8mm means 5m and 8dm and 4cm and 8mm. So, we need to add them while combining them.