Final answer:
Dividing 25% of a number is the same as dividing the number by 1/4 because 25% is equivalent to 1/4, and dividing by a fraction is the same as multiplying by its reciprocal.
Step-by-step explanation:
Is Dividing by 25% the Same as Dividing by 1/4?
Dividing 25% of a number is indeed the same as dividing the number by 1/4. Let's take a closer look to understand why this is true. To calculate 25% of a number, you would multiply the number by 0.25 or 1/4. Now, let's consider division. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/4 is 4, so dividing by 1/4 is the same as multiplying by 4. Knowing this, dividing a number by 1/4 is essentially the same operation as finding 25% of it.
For example, if we have a number 'x', and we want to find 25% of it, we calculate x * 1/4. Conversely, if we're dividing 'x' by 1/4, we're performing the operation x * 4, because dividing by 1/4 is the same as multiplying by its reciprocal, which is 4. These operations yield the same result, demonstrating that dividing by 25% (which is 1/4) is the same as dividing a number by 1/4.
To illustrate further, let's think about a scenario where you know one-half of one-half is one quarter. This intuitive understanding helps us recognize that the processes of finding a percentage (which is a fraction of 100) and dividing by a fraction are interconnected through the use of multiplication and reciprocals.