Final answer:
Dividing both the numerator and denominator of the fraction 8/20 by 2 gives you the equivalent ratio 4/10. This process does not change the value of the fraction and reveals that division by a number is the same as multiplying by its reciprocal.
Step-by-step explanation:
If you divide the numerator (8) and the denominator (20) of the fraction 8/20 by the same number, in this case 2, you will indeed obtain an equivalent ratio. Dividing 8 by 2 gives you 4, and dividing 20 by 2 gives you 10, resulting in the ratio 4/10. Importantly, both 8/20 and 4/10 represent the same value when simplified; they are equivalent fractions.
Multiplication and division can be thought of as inverse operations. When you divide by a number, it is the same as multiplying by its reciprocal. So, dividing both the numerator and the denominator of a fraction by the same non-zero number will not change the value of that fraction, it just simplifies it. This concept is crucial in understanding proportions and equivalent ratios. For example, 8 fl oz = 1 cup is an example of a unit equivalence. If you have 20 fluid ounces, and you need to find out how many cups that is, you divide 20 by 8, which yields 2 1/2 cups.