Final answer:
To simplify the expression 2(1/2) ÷ 2(1/4), we convert the division into multiplication by the reciprocal of the second term to get 1 × ⅔, which simplifies to 4/3.
Step-by-step explanation:
To simplify the expression 2(1/2) ÷ 2(1/4), we can understand that dividing by a fraction is the same as multiplying by its reciprocal. The given expression can be written as 2 × ½ divided by 2 × ¼, which simplifies to 1 ÷ ¾. By flipping the second fraction to find its reciprocal, we get 1 × ⅔.
When multiplying fractions, we multiply the numerators and the denominators separately. So, 1 × 4 in the numerator and 1 × 3 in the denominator gives us 4/3 as the simplified result. Simplification in this context means performing the same operation on both sides of an equation to maintain equality and using multiplication of fractions to arrive at the simplest form of an expression.