Final answer:
To solve 4 divided by one fourth, multiply 4 by the reciprocal of one fourth, which gives 16. Scaling and proportions involve setting up and solving ratios to find missing values, such as measurements or dimensions.
Step-by-step explanation:
To solve 4 ÷ one fourth, remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of one fourth (1/4) is four (4/1). So the problem becomes 4 × 4, which equals 16. This is a basic arithmetic operation involving fractions and multiplication.
Let's apply a similar approach to a scaled dimension problem. For example, if given a scale factor of 1:4 and a scale measurement of 4, to find the actual dimension, you would set up a proportion such as 1:4 = 4:x. Solving this proportion involves cross-multiplying to find the value of 'x', which represents the actual dimension in this case.
Proportions are commonly used to solve problems involving scaled measurements or ratios. Whether you are converting gallons to quarts or determining the size of an object based on its scale factor, properly setting up and solving proportions is key to finding the correct answer.
Consider an example with volumes: If you have a ratio of 1 gallon to 4 quarts, to find out how many quarts are in 3 gallons, you would set up and solve the proportion 1 gallon/4 quarts = 3 gallons/x quarts.