Question
An average stenographer can type 510 words in 180 seconds. Write the ratio of words to seconds as a simplified fraction. Provide your answer below: \( \frac{\square \text { words }}{\square} \) seconds
Ask by Donnelly Warner. in the United States
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ratio of words to seconds is \( \frac{17 \text{ words}}{6 \text{ seconds}} \).
Solution
1. We start with the ratio of words to seconds:
\[
\frac{510 \text{ words}}{180 \text{ seconds}}
\]
2. To simplify, we divide both the numerator and denominator by their greatest common divisor. In this case, both 510 and 180 are divisible by 30.
3. Dividing the numerator and denominator by 30:
\[
510 \div 30 = 17 \quad \text{and} \quad 180 \div 30 = 6
\]
4. The simplified ratio is:
\[
\frac{17 \text{ words}}{6 \text{ seconds}}
\]
Thus, the final answer is
\[
\frac{17 \text{ words}}{6 \text{ seconds}}
\]
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The Deep Dive
The stenographer types 510 words in 180 seconds. To find the ratio of words to seconds, we can express it as \( \frac{510 \text{ words}}{180 \text{ seconds}} \). Simplifying this fraction involves finding the greatest common divisor (GCD) of 510 and 180, which is 30. Dividing both the numerator and the denominator by 30 gives us \( \frac{17 \text{ words}}{6 \text{ seconds}} \). So, the answer is: \( \frac{17 \text{ words}}{6} \) seconds