Question

what is the value of $3\frac{1}{3} \div \frac{2}{3}$?
show your work on the scratchpad.

• hint- when we divide fractions, you do not common denominators. here you have a mixe you need to change this to an improper fractio then, keep the total, and then multiple by the reciprocal..think.. keep< change< flip!

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(3\frac{1}{3}\) can be converted 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 \(3\frac{1}{3}\), we have \(a = 3\), \(b = 1\), \(c = 3\). Then \(\frac{3\times3+ 1}{3}=\frac{9 + 1}{3}=\frac{10}{3}\).

Step2: Apply keep - change - flip for division of fractions

When dividing fractions, we use the rule: \( \frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}\) (keep the first fraction, change division to multiplication, flip the second fraction). Here, the first fraction is \(\frac{10}{3}\) and the second fraction is \(\frac{2}{3}\). So \(\frac{10}{3}\div\frac{2}{3}=\frac{10}{3}\times\frac{3}{2}\).

Step3: Multiply the fractions

To multiply fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\). For \(\frac{10}{3}\times\frac{3}{2}\), we have \(a = 10\), \(b = 3\), \(c = 3\), \(d = 2\). Then \(\frac{10\times3}{3\times2}=\frac{30}{6}\).

Step4: Simplify the result

Simplify \(\frac{30}{6}\) by dividing the numerator and the denominator by their greatest common divisor, which is 6. \(\frac{30\div6}{6\div6}=5\).

Answer:

\(5\)