Final answer:
To solve the division problem 500 divided by 2/3, we multiply 500 by the reciprocal of 2/3, which is 3/2, resulting in an answer of 750 feet. Scale ratios and unit conversions, such as inches to feet, require consistent units and can be solved using proportions and cross-multiplication.
Step-by-step explanation:
Understanding Division and Multiplication in Context
When faced with the equation 500 divided by 2/3, it can also be expressed as 500 multiplied by the reciprocal of 2/3. To find the reciprocal of a fraction, you simply flip the numerator and the denominator. In this case, the reciprocal of 2/3 is 3/2. Therefore, 500 divided by 2/3 is equivalent to 500 multiplied by 3/2. This results in:
500 × 3/2 = 750
Thus, the answer is 750 feet. When dealing with proportions and unit scales, such as converting inches to feet or vice versa, the process involves setting up ratios and using cross-multiplication to find the missing value.
For example, the unit scale 1/2 inch equals 5 feet can be written as a ratio for scaling purposes. If there's a need to convert 5 feet to inches, the following equivalence is used:
1 foot = 12 inches
Therefore:
5 feet × 12 inches/foot = 60 inches
When dealing with different units of measurement, it's important to keep the units consistent to properly form and solve proportions. Following this method allows for accurate scale drawings and unit conversions.