John had $2/3$ of his homework complete, Sarah had $5/10$, Alex $7/8$, and Michelle $1/2$. Who completed the most of the homework assignment?
Answer (1)
Convert each fraction to a decimal: 3 2 ≈ 0.667 , 10 5 = 0.5 , 8 7 = 0.875 , 2 1 = 0.5 .
Compare the decimal values.
Identify the largest decimal value: 0.875 .
Conclude that Alex completed the most homework: Alex
Explanation
Problem Analysis We need to determine who completed the most homework given the fractions of homework completed by John, Sarah, Alex, and Michelle.
Listing Fractions First, let's list the fractions of homework completed by each person:
John: 3 2 Sarah: 10 5 Alex: 8 7 Michelle: 2 1
Converting to Decimals To compare these fractions, we can convert them to decimals:
John: 3 2 ≈ 0.667 Sarah: 10 5 = 0.5 Alex: 8 7 = 0.875 Michelle: 2 1 = 0.5
Comparing Decimals Now, we compare the decimal values:
John: 0.667 Sarah: 0.5 Alex: 0.875 Michelle: 0.5
We can see that Alex completed the most homework with 0.875 .
Conclusion Therefore, Alex completed the most of the homework assignment.
Examples
Understanding fractions and comparing them is essential in many real-life situations. For example, when baking, you might need to compare different amounts of ingredients to ensure the recipe turns out correctly. Similarly, in sports, comparing fractions can help determine which player has the best performance based on their success rate. This problem demonstrates a fundamental skill in mathematics that has practical applications in various fields.
