Divide: $1 6 ) \overline{ 6 , 6 7 2 }$
A) 416
B) 537
C) 367
D) 417
E) 517

Question

Divide:   $1 6 ) \overline{ 6 , 6 7 2 }$
A) 416
B) 537
C) 367
D) 417
E) 517

Quizplus · Accepted Answer

To divide a number by 16, we can multiply it by $\frac{1}{16}$. We can start by estimating the approximate value of the fraction $\frac{1}{16}$ by dividing 1 by 16:

$$\frac{1}{16} \approx 0.06$$

We can use this to estimate the quotient. Looking at the digits of the dividend, we can try dividing 66 by 0.06:

$$\frac{66}{0.06} = 1100$$

This is close to the thousands place of the quotient, so we can try using 1100 as our estimate.

$$
equire{enclose}
\begin{array}{r r@{}l}
&1&.\
16&\enclose{longdiv}{1}&6.67 \
\multicolumn{2}{r}{1}&6\
\multicolumn{2}{r}{}&7\phantom{0} \
16&\enclose{longdiv}{6} &6.72\
\multicolumn{2}{r}{6}&6 \
\multicolumn{2}{r}{}&207\phantom{.} \
16&\enclose{longdiv}{5} &1.67\
\multicolumn{2}{r}{1}&6\
\multicolumn{2}{r}{}&7 \
\end{array}
$$

The closest answer choice to 167 is 417, so we choose $\boxed{	extbf{(D)}}$.

Divide 16)6,672‾1 6 ) \overline{ 6 , 6 7 2 }16)6,672​

Divide $1 6 ) \overline{ 6 , 6 7 2 }$