Final answer:
The correct answer is option 3. To find which of the fractions 3/5, 5/8, 3/4, and 5/10 is greatest, we can convert them to decimals or find a common denominator. Both methods show that 3/4 is the largest fraction.
Step-by-step explanation:
To determine which fraction is greater out of 3/5, 5/8, 3/4, and 5/10, we can compare each fraction by converting them to decimals or finding a common denominator.
Firstly, let's convert the fractions to decimals:
- 3/5 = 0.6
- 5/8 = 0.625
- 3/4 = 0.75
- 5/10 = 0.5
By comparing these decimals, it is clear that 3/4 (which converts to 0.75) is the largest fraction.
If we choose to find a common denominator, let's pick 40, as it is a multiple of 5, 8, 4, and 10:
- 3/5 = 24/40
- 5/8 = 25/40
- 3/4 = 30/40
- 5/10 = 20/40
Using the common denominator method, we see that 3/4, or 30/40, is still the greatest fraction.
Your intuitive sense of fractions can also aid in determining that, for example, 3/4 is more than half (0.5) while others are closer to half or just over. Using intuition, alongside mathematical methods, ensures accurate comparison of fractions.