Case Study Questions on Rational Numbers for Class 7
Rational numbers are numbers that can be expressed as a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. Understanding rational numbers is crucial for developing strong mathematical skills. Here are some engaging case study questions along with detailed answers.
Question 1: Comparing Rational Numbers
Rita and Raj have been discussing their scores in a quiz. Rita scored 3/4 and Raj scored 5/8. Who scored higher?
Answer:
- Convert both scores to a common denominator:
- The least common multiple of 4 and 8 is 8.
- Rita's score: 3/4 = (3*2)/(4*2) = 6/8
- Raj's score: 5/8 remains the same.
- Compare the scores:
- 6/8 (Rita) is greater than 5/8 (Raj).
- Conclusion: Rita scored higher than Raj.
Question 2: Adding Rational Numbers
A recipe requires 1/3 kg of sugar and 1/4 kg of flour. How much total weight of ingredients is used?
Answer:
- Find a common denominator:
- The least common multiple of 3 and 4 is 12.
- Convert fractions:
- Sugar: 1/3 = 4/12
- Flour: 1/4 = 3/12
- Add the fractions:
- Total = 4/12 + 3/12 = 7/12 kg.
- Conclusion: The total weight of the ingredients used is 7/12 kg.
Question 3: Subtracting Rational Numbers
Tom has 2/5 of a liter of juice. He drinks 1/10 of a liter. How much juice is left?
Answer:
- Find a common denominator:
- The least common multiple of 5 and 10 is 10.
- Convert fractions:
- Tom's juice: 2/5 = 4/10
- Subtract the amount drunk:
- Remaining = 4/10 - 1/10 = 3/10 liters.
- Conclusion: Tom has 3/10 liters of juice left.
These case study questions illustrate the application of rational numbers in real-life scenarios while enhancing understanding and problem-solving skills.