Final answer:
Andy's strategy is correct because dividing a fraction by itself is equivalent to multiplying it by its reciprocal, which yields unity. Multiplying (4/5) by its reciprocal (5/4) is the same as dividing (4/5) by (4/5), resulting in the answer of 1.
Step-by-step explanation:
Andy's strategy of solving (4/5) ÷ (4/5) by multipliying (4/5) × (5/4) will indeed work. This is because dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a number or fraction is simply one divided by that number or fraction. In the case of (4/5), the reciprocal is (5/4). Therefore, when Andy multiplies (4/5) by (5/4), he is effectively performing the division operation (4/5) ÷ (4/5), which results in 1, or unity. This is an application of the mathematical property that states multiplication or division by a number's reciprocal yields unity.