Question

divide $6\frac{2}{3} \div 3\frac{1}{2}$. write your answer as a mixed number.\
$\bigcirc\\ 1\frac{19}{21}$\
$\bigcirc\\ \frac{40}{21}$\
$\bigcirc\\ 23\frac{1}{3}$\
$\bigcirc\\ 9\frac{3}{5}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(6\frac{2}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(6\frac{2}{3}\), we have \(a = 6\), \(b = 2\), \(c = 3\). Then \(6\times3+2 = 20\), so \(6\frac{2}{3}=\frac{20}{3}\).

Next, convert \(3\frac{1}{2}\) to an improper fraction. Using the same formula, \(a = 3\), \(b = 1\), \(c = 2\). Then \(3\times2 + 1=7\), so \(3\frac{1}{2}=\frac{7}{2}\).

Step2: Divide the improper fractions

Dividing fractions is done by multiplying the first fraction by the reciprocal of the second fraction. So \(\frac{20}{3}\div\frac{7}{2}=\frac{20}{3}\times\frac{2}{7}\).

Multiply the numerators and denominators: \(20\times2 = 40\) and \(3\times7 = 21\), so we get \(\frac{40}{21}\).

Step3: Convert the improper fraction to a mixed number

To convert \(\frac{40}{21}\) to a mixed number, divide 40 by 21. \(21\times1 = 21\), and \(40 - 21 = 19\). So \(\frac{40}{21}=1\frac{19}{21}\).

Answer:

\(1\frac{19}{21}\)