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Explain the concept of direct and inverse proportions with examples from the given text.
Explain the concept of direct and inverse proportions with examples from the given text.
Direct proportion refers to a situation in which two quantities change in the same direction, meaning that as one quantity increases, the other also increases, and vice versa. Inverse proportion, on the other hand, refers to a situation in which two quantities change in opposite directions, meaning that as one quantity increases, the other decreases, and vice versa. An example of direct proportion from the text is the increase in the number of articles purchased leading to an increase in the total cost. An example of inverse proportion from the text is the increase in the speed of a vehicle leading to a decrease in the time taken to cover the same distance.
How can the concept of direct proportion be applied to Mohan's tea preparation?
How can the concept of direct proportion be applied to Mohan's tea preparation?
The concept of direct proportion can be applied to Mohan's tea preparation by understanding that as the quantity of tea to be made increases (for five persons instead of just Mohan and his sister), the quantities of water, sugar, tea leaves, and milk also need to increase in direct proportion. This means that the quantity of each item needed will be directly proportional to the number of persons for whom the tea is being prepared.
Provide five real-life situations where a change in one quantity leads to a change in another quantity, as mentioned in the text.
Provide five real-life situations where a change in one quantity leads to a change in another quantity, as mentioned in the text.
- Increase in the number of articles purchased leads to an increase in the total cost.
- More money deposited in a bank leads to more interest earned.
- Increase in the speed of a vehicle leads to a decrease in the time taken to cover the same distance.
- More workers for a given job lead to less time taken to complete the work.
- Increase in the quantity of ingredients leads to an increase in the quantity of tea prepared.
Explain how the cost of 3 kg of sugar can be calculated using the concept of direct proportion.
Explain how the cost of 3 kg of sugar can be calculated using the concept of direct proportion.
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How can the concept of inverse proportion be applied to the time taken to arrange chairs for an assembly?
How can the concept of inverse proportion be applied to the time taken to arrange chairs for an assembly?
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Study Notes
Direct and Inverse Proportions
- Direct proportion occurs when two quantities increase or decrease together. For example, if the number of items increases, the total cost increases proportionally.
- Inverse proportion happens when one quantity increases while the other decreases. For instance, if speed increases, the time taken for a journey decreases.
Application of Direct Proportion in Tea Preparation
- The amount of tea leaves required is directly proportional to the number of cups prepared. If the number of cups doubles, the quantity of tea leaves must also double.
- If Mohan uses 10 grams of tea leaves for one cup, for four cups, he will need 40 grams.
Real-Life Situations Demonstrating Proportional Changes
- A chef adjusts ingredients for larger meals; more diners mean more food preparation.
- The distance a car can travel increases with more fuel; more fuel means a greater distance.
- The time taken to complete a task decreases if more workers are employed; more workers yield quicker completion.
- A student’s knowledge improves with more study hours; more hours of study enhance understanding.
- A gardener uses more water as the number of plants increases; more plants require more water.
Calculating Cost Using Direct Proportion
- The cost of sugar can be determined by establishing a rate; for example, if 1 kg of sugar costs $2, then the cost for 3 kg is calculated as:
- Cost for 3 kg = Cost for 1 kg × 3
- Hence, 3 kg of sugar costs $2 × 3 = $6.
Application of Inverse Proportion in Time for Arranging Chairs
- The time taken to arrange chairs for an assembly is inversely proportional to the number of people available. With more helpers, the time required decreases.
- If 10 people can arrange chairs in 1 hour, 20 people can complete the same task in 30 minutes.
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Description
Test your understanding of direct and inverse proportions with this quiz. Explore real-life situations and solve problems related to the quantities of items needed for different group sizes.
