Final answer:
To find the equivalent expression to 40 ÷ 1/4, we multiply 40 by the reciprocal of 1/4, which is 4, resulting in 160. When dealing with scale factors, to calculate the actual dimension from the scale dimension, a proportion is used.
Step-by-step explanation:
To find an expression equivalent to 40 ÷ 1/4, we need to understand that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 1/4 is 4/1 (or simply 4). Therefore, the calculation becomes 40 × 4, which equals 160.
When solving this kind of problem, one method to rearrange algebraically is to divide by a given number on both sides of the equals sign and then to multiply both sides of the equals sign by the same number, which in this case would be irrelevant since we are not solving an equation but performing a direct calculation.
Using Proportions in Scale Measurements
In the context of scale measurements, if the scale factor is 1:4 and we have a scale dimension of 4, the actual dimension can be calculated using the proportion 1:4 = 4:x. To find x, we multiply both sides of the equation by the actual dimension, giving us x = 4 × 4, which is x = 16.