Question
Read the following sentence: A survey showed that \( 50 \% \) of people prefer eating Italian food, \( 33,3 \% \) prefer Indian food and \( 15 \% \) like Chinese food. The rest had no preference. Replace the percentages with: a) decimals b) fractions
Ask by Powers Ray. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
*Rewritten Sentence:*
*A survey showed that **0.50** of people prefer eating Italian food, **0.333** prefer Indian food, and **0.15** like Chinese food. The rest had no preference.*
*Rewritten Sentence:*
*A survey showed that **\(\frac{1}{2}\)** of people prefer eating Italian food, **\(\frac{1}{3}\)** prefer Indian food, and **\(\frac{3}{20}\)** like Chinese food. The rest had no preference.*
Solution
Sure! Let's replace the percentages in the sentence with decimals and fractions.
### Original Sentence:
*A survey showed that \( 50 \% \) of people prefer eating Italian food, \( 33.3 \% \) prefer Indian food and \( 15 \% \) like Chinese food. The rest had no preference.*
---
### a) **Replacing Percentages with Decimals:**
To convert percentages to decimals, divide each percentage by 100.
- \( 50\% = 0.50 \)
- \( 33.3\% = 0.333 \)
- \( 15\% = 0.15 \)
**Rewritten Sentence:**
*A survey showed that **0.50** of people prefer eating Italian food, **0.333** prefer Indian food, and **0.15** like Chinese food. The rest had no preference.*
---
### b) **Replacing Percentages with Fractions:**
Convert each percentage to its simplest fractional form.
- \( 50\% = \frac{50}{100} = \frac{1}{2} \)
- \( 33.3\% \approx \frac{33.3}{100} = \frac{1}{3} \) *(since 33.3% is approximately one third)*
- \( 15\% = \frac{15}{100} = \frac{3}{20} \)
**Rewritten Sentence:**
*A survey showed that **\(\frac{1}{2}\)** of people prefer eating Italian food, **\(\frac{1}{3}\)** prefer Indian food, and **\(\frac{3}{20}\)** like Chinese food. The rest had no preference.*
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Explain 
Simplify this solution The Deep Dive
In decimal form, the preferences would be represented as: 0.50 for Italian food, 0.333 for Indian food, and 0.15 for Chinese food. The remaining percentage of people with no preference can be calculated as: \( 1 - (0.50 + 0.333 + 0.15) = 0.017 \) or approximately 0.02. As fractions, the preferences translate to: \( \frac{1}{2} \) for Italian food, \( \frac{1}{3} \) for Indian food, and \( \frac{3}{20} \) for Chinese food. The remainder with no preference can be reflected as: \( 1 - \left( \frac{1}{2} + \frac{1}{3} + \frac{3}{20} \right) = \frac{1}{60} \), or about 1.67%.
