Julie can compare her test scores by comparing the fractions representing her correct answers on each test. The two fractions to compare are:

• Math test: $\frac{21}{23}$ (21 out of 23 questions correct)
• Science test: $\frac{29}{32}$ (29 out of 32 questions correct)

Step 1: Convert fractions to decimals

An easy way to compare the fractions is to convert them into decimal form by dividing the numerator by the denominator.

$\frac{21}{23} \approx 0.913$ $\frac{29}{32} \approx 0.906$

So, $\frac{21}{23} \approx 0.913$ and $\frac{29}{32} \approx 0.906$.

Step 2: Compare the decimals

Julie scored approximately 91.3% on the math test and approximately 90.6% on the science test. Therefore, Julie performed slightly better on the math test.

Explaining the comparison of 21 and 29:

Although Julie answered more questions correctly on the science test (29 vs. 21), the percentages differ because the total number of questions is different in each case. To directly compare 29 and 21 without considering the total number of questions would be misleading, as it doesn’t account for the size of each test. The fraction $\frac{21}{23}$ represents a higher percentage of questions answered correctly compared to $\frac{29}{32}$.

Conclusion:

Julie got a higher score on her math test than on her science test.

Would you like further details or a step-by-step breakdown of any part of this?

Here are five related questions for deeper understanding:

1. How can you compare fractions using cross-multiplication?
2. What are some other methods to compare fractions without converting to decimals?
3. How can percentages help in comparing different test scores?
4. Why is it important to consider the total number of questions in a test when comparing scores?
5. How could Julie improve her scores based on this comparison?

Tip: When comparing fractions, converting them to decimals or using cross-multiplication can simplify the process!