Simplifying Fractions

Task goals

• Read a simplify-bar diagram to see fine equal parts bundled by a common factor into coarser simplified parts.
• Find the highest common factor (HCF) of a numerator and denominator and use it to simplify a fraction in one step.
• Recognise and justify when a fraction is already in simplest form (HCF of numerator and denominator is 1).
• Compare simplifying in one step (by the HCF) against simplifying in several smaller steps, confirming both reach the same final answer.
• Critique a partial-simplification claim where a fraction was divided by a common factor that was not the highest one.
• Distinguish simplifying (always dividing to the smallest form) from generating an equivalent fraction (which can scale either way).