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On Sunday, of the dogs seen in the park were on leashes. On Wednesday, of the dogs in the same park were on leashes. Which day had a greater fraction of dogs on leashes?A)SundayB)Wednesday
Full solution
Q. On Sunday, of the dogs seen in the park were on leashes. On Wednesday, of the dogs in the same park were on leashes. Which day had a greater fraction of dogs on leashes?A)SundayB)Wednesday
- Understand fractions given: Understand the fractions given for each day.On Sunday, the fraction of dogs on leashes is .On Wednesday, the fraction of dogs on leashes is .We need to compare these two fractions to determine which is greater.
- Compare fractions directly: Compare the two fractions directly.Since the denominators are different and , we cannot directly compare the fractions by looking at the numerators. We need to find a common denominator or use another method to compare the fractions.
- Use cross-multiplication: Use cross-multiplication to compare the fractions.Cross-multiply the fractions to compare their sizes without finding a common denominator. Multiply the numerator of the first fraction by the denominator of the second fraction and vice versa. compared to becomes: (for Sunday) (for Wednesday)
- Determine greater product: Determine which product is greater.The product for Sunday is , and the product for Wednesday is . Since is greater than , the fraction is greater than .
- Conclude greater fraction day: Conclude which day had a greater fraction of dogs on leashes. Since is greater than , Wednesday had a greater fraction of dogs on leashes than Sunday.
