Elena is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Elena spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Elena get a higher ratio of correctly spelled words to total words?

Answer 1

To find out which test Elena had a higher ratio of correctly spelled words to total words, we need to calculate the ratio for both tests.

Last week's test:

• Correctly spelled words: 16
• Total words: 20

The ratio for last week can be calculated as follows: \[ \text{Ratio}{\text{last week}} = \frac{\text{Correctly spelled words}}{\text{Total words}} = \frac{16}{20} \] To simplify \(\frac{16}{20}\): \[ \frac{16 \div 4}{20 \div 4} = \frac{4}{5} \] So, \[ \text{Ratio}{\text{last week}} = 0.8 \]

This week's test:

• Correctly spelled words: 13
• Total words: 15

The ratio for this week can be calculated as follows: \[ \text{Ratio}{\text{this week}} = \frac{\text{Correctly spelled words}}{\text{Total words}} = \frac{13}{15} \] This fraction does not simplify further, so we calculate its decimal value: \[ \text{Ratio}{\text{this week}} \approx 0.8667 \]

Comparison of the ratios:

• Last week's ratio: \(0.8\)
• This week's ratio: \(0.8667\)

Since \(0.8667\) is greater than \(0.8\), we conclude that Elena had a higher ratio of correctly spelled words to total words on this week's test.

Therefore, Elena got a higher ratio on this week's test.