Short Questions
Question: What is meant by a proportional relationship?
Answer: A proportional relationship is one in which two or more quantities change by the same factor.
Question: Define a ratio.
Answer: A ratio is a comparison of two quantities written in the form a : b.
Question: What condition must be satisfied for two ratios to be proportional?
Answer: Two ratios a : b and c : d are proportional if
a × d = b × c.
Question: What is a Representative Fraction (RF)?
Answer: RF is the ratio between the distance on a map and the actual distance on the ground.
Question: What does the ratio 1 : 60,00,000 represent in a map?
Answer: It means 1 cm on the map represents 60,00,000 cm (60 km) in reality.
Question: Can a ratio have more than two terms?
Answer: Yes, a ratio can have more than two terms if all quantities change by the same factor.
Question: What is meant by dividing a quantity in a given ratio?
Answer: It means splitting a quantity into parts according to the given ratio.
Question: What is a pie chart?
Answer: A pie chart is a circular diagram used to represent data as parts of a whole.
Question: What is direct proportion?
Answer: Two quantities are in direct proportion if they increase or decrease together in the same ratio.
Question: What is inverse proportion?
Answer: Two quantities are in inverse proportion if one increases while the other decreases in such a way that their product remains constant.
Long Questions
1. Explain proportionality and how to check it.
Answer: Proportionality refers to a relationship between two ratios where they are equal. If two quantities change in such a way that their ratio remains constant, they are said to be proportional.
To check whether two ratios a : b and c : d are proportional, we use cross multiplication:
a × d = b × c.
If both products are equal, the ratios are proportional. For example, 2 : 4 and 3 : 6 are proportional because
2 × 6 = 4 × 3 = 12.
2. Explain Representative Fraction (RF) and its importance.
Answer: Representative Fraction (RF) is the ratio between the distance on a map and the actual distance on the ground. It is written in the form 1 : n.
It helps us understand how much the real-world distance has been reduced on the map. For example, if RF is 1 : 60,00,000, it means 1 cm on the map represents 60 km in reality.
RF is useful for calculating actual distances between places using maps.
3. Explain ratios with more than two terms.
Answer: A ratio can have more than two terms when more than two quantities are compared. For example, 2 : 3 : 5 compares three quantities.
Such ratios are proportional if all terms are multiplied or divided by the same number. For example, 2 : 3 : 5 is proportional to 4 : 6 : 10.
This type of ratio is useful in mixing ingredients or dividing quantities.
4. Explain how to divide a quantity in a given ratio.
Answer: To divide a quantity in a given ratio:
- Add all parts of the ratio.
- Divide the total quantity by the sum.
- Multiply the result by each part of the ratio.
For example, divide 60 in the ratio 2 : 3.
Sum = 2 + 3 = 5
Each unit = 60 ÷ 5 = 12
Parts = 2 × 12 = 24 and 3 × 12 = 36
Thus, the quantity is divided into 24 and 36.
5. Differentiate between direct and inverse proportion.
Answer: In direct proportion, two quantities increase or decrease together. Their ratio remains constant. For example, if the number of items increases, the cost also increases.
In inverse proportion, one quantity increases while the other decreases. Their product remains constant. For example, if speed increases, time taken decreases for a fixed distance.
Thus, direct proportion involves same direction change, while inverse proportion involves opposite direction change.
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