Question 1 - Mental Math - Chapter 3 Class 6 - Number Play (Ganita Prakash)

Transcript

Question 1 Write an example for each of the below scenarios whenever possible. Could you find examples for all the cases? If not, think and discuss what could be the reason. Make other such questions and challenge your classmates.1. 5-digit + 5-digit to give a 5-digit sum more than 90,250 Possible. Example: 50,000 + 45,000 = 95,000. The sum is a 5-digit number and is greater than 90,250. 2. 5-digit + 3-digit to give a 6-digit sum Possible. Example: 99,999 + 100 = 100,099. By adding to the largest 5-digit number, the sum tips over into the 6-digit range (100,000 and above). 3. 4-digit + 4-digit to give a 6-digit sum Impossible. Reason: The largest possible 4-digit number is 9,999 The maximum possible sum you can get is 9,999 + 9,999 = 19,998, which is a 5-digit number. You can never reach the 6-digit range. 4. 5-digit + 5-digit to give a 6-digit sum Possible. Example: 60,000 + 50,000 = 110,000. Any two 5-digit numbers whose sum is 100,000 or more will work. 5. 5-digit + 5-digit to give 18,500 Impossible. Reason: The smallest 5-digit number is 10,000. The minimum possible sum you can get by adding two 5-digit numbers is 10,000 + 10,000 = 20,000. 8. 5-digit - 4-digit to give a 4-digit difference Possible. Example: 15,000 - 8,000 = 7,000. 9. 5-digit - 5-digit to give a 3-digit difference Possible. Example: 45,800 - 45,500 = 300. To get a small 3-digit difference, the two 5-digit numbers must be very close to each other. 10. 5-digit - 5-digit to give 91,500 Impossible. Reason: To get a difference this large, the first number would have to be a 6-digit number. It is impossible to get a sum as low as 18,500. 6. 5-digit - 5-digit to give a difference less than 56,503 Possible. Example: 65,000 - 50,000 = 15,000. As long as the two numbers are reasonably close, the difference will be less than 56,503. 7. 5-digit - 3-digit to give a 4-digit difference Possible. Example: 10,500 - 600 = 9,900. Starting with a small 5-digit number and subtracting a 3-digit number can result in a 4-digit number. For example, if you subtract the smallest 5-digit number (10,000) from another number to get 91,500, that number would have to be 10,000 + 91,500 = 101,500, which is a 6-digit number. The maximum possible difference between two 5-digit numbers is 99,999 - 10,000 = 89,999.