Question

write $3\frac{6}{7}$ as an improper fraction in lowest terms.
$\frac{18}{7}$
$\frac{18}{21}$
$\frac{9}{7}$
$\frac{27}{7}$

Explanation:

Step1: Recall the formula for converting a mixed number to an improper fraction.

To convert a mixed number \( a\frac{b}{c} \) to an improper fraction, we use the formula \( \frac{a\times c + b}{c} \), where \( a \) is the whole number part, \( b \) is the numerator of the fractional part, and \( c \) is the denominator of the fractional part.

Step2: Apply the formula to \( 3\frac{6}{7} \).

Here, \( a = 3 \), \( b = 6 \), and \( c = 7 \).
First, calculate \( a\times c + b \):
\( 3\times7 + 6 = 21 + 6 = 27 \).
Then, the improper fraction is \( \frac{27}{7} \) (since the denominator \( c \) remains 7).

Answer:

D. \(\frac{27}{7}\) (assuming the last option is D, as the options are: A. \(\frac{18}{7}\), B. \(\frac{18}{21}\), C. \(\frac{9}{7}\), D. \(\frac{27}{7}\))