Reciprocals

Task goals

• Find the reciprocal of a unit fraction such as $\dfrac{1}{2}$ or $\dfrac{1}{3}$ by swapping the numerator and denominator.
• Find the reciprocal of a non-unit fraction such as $\dfrac{4}{7}$ by flipping the numerator and denominator to get $\dfrac{7}{4}$.
• Find the reciprocal of a whole number by first writing it as a fraction over $1$, e.g. $5=\dfrac{5}{1}$, so its reciprocal is $\dfrac{1}{5}$.
• Check whether two given numbers are reciprocals of each other by confirming their product equals $1$.
• Use reasoning about reciprocals to compare sizes (e.g. which of two reciprocals is greater) or to find a missing numerator/denominator so a stated pair are reciprocals.
• Explain in words why swapping the numerator and denominator of a number produces a value that multiplies with the original to give $1$, including the special case that $1$ is its own reciprocal.