Final answer:
To rename 1/2 as tenths, we determine the equivalent fraction with a denominator of 10, which is 5/10. Using intuition, we can understand this by visualizing a pie cut into 10 equal pieces, where 5 pieces would represent half of the pie. Additionally, to find one-eighth of 1,000, we can multiply by the reciprocal of 8 to easily get 125.
Step-by-step explanation:
Renaming 1/2 as Tenths
To rename the fraction 1/2 as tenths, we want to find an equivalent fraction with a denominator of 10. Since 1/2 is the same as 5/10, we have effectively renamed 1/2 in terms of tenths.
Understanding Fractions Using Intuition
If you have a strong intuitive sense for fractions, such as understanding that half a pie is larger than a third of a pie, then renaming fractions to a specific denominator like tenths becomes easier. Think of 1/2 as 5 pieces out of a pie that is divided into 10 equal pieces. This intuitive approach helps in visualizing why 1/2 is the same as 5/10.
Finding One-Eighth of 1,000
To find what one eighth of 1,000 is, you can multiply 1,000 by the reciprocal of 8, which is 1/8. This simplifies the process, leading to the answer 125. It's critical to approach this logically, noting that 125 is close to 100 (one-tenth of 1,000), which supports the correctness of the result being 125