Dividing fractions

Task goals

• Divide one fraction by another using the keep, change, flip (KCF) rule: keep the first fraction, change $\div$ to $\times$, and flip (take the reciprocal of) the second fraction, e.g. $\dfrac{1}{2}\div\dfrac{1}{4}$.
• Divide a whole number by a fraction, and a fraction by a whole number, by first rewriting the whole number as a fraction over $1$ before applying KCF.
• Simplify the resulting fraction and convert an improper fraction to a mixed number where appropriate.
• Explain why dividing by a fraction smaller than $1$ gives an answer larger than the original number, e.g. why $10\div\dfrac{1}{2}>10$.
• Solve a word problem that requires dividing a fraction by a fraction, such as finding how many equal fractional pieces fit into a given length.
• Find a missing fraction in a division equation such as $\dfrac{2}{3}\div x=\dfrac{8}{9}$, and check the answer is sensible.