Final answer:
To find the number of groups of ⅔ in 1, we divide 1 by ⅔ resulting in 1.4 groups. To divide 8 by ⅔, we multiply 8 by the reciprocal of ⅔ (⁷⁄₅) to get 11.2. For precision, round numbers to the hundredths place if needed, like rounding 201.867 to 201.87.
Step-by-step explanation:
The question is asking how many groups of ⅔ (five sevenths) are in 1 (one whole), which is a division problem that can be solved using the concept of dividing fractions. To find out how many groups of ⅔ are in 1, you have to divide 1 by ⅔. This is equivalent to multiplying 1 by the reciprocal of ⅔, which is ⁷⁄₅ (seven fifths). Multiplying 1 by ⁷⁄₅, you get ⁷⁄₅, which means there are 1⁷⁄₅ or 1.4 groups of ⅔ in 1.
The second part of the question involves evaluating 8 ÷ ⅔. To do this, you multiply 8 by the reciprocal of ⅔, which is ⁷⁄₅, resulting in 11⁴⁄₅. When written as a decimal, this is equal to 11.2. However, if we were to calculate it with a bit more precision, depending on your calculator, you might obtain a longer decimal number such as 201.867, but as instructed, we have to round it to the hundredths place. Since the digit to be dropped (7) is greater than 5, we round up, resulting in a final answer of 201.87.