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Find the sum by suitable rearrangement: 837+208+363 .

Find the sum by suitable rearrangement: 837+208+363
.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days ago
Here, we need to find the sum of the given numbers by a suitable arrangement. We will create three arrangements, adding a pair of 2 numbers out of the 3 given numbers. We will check the digit at the unit's place in the sum of those 2 numbers. If it is easier to add the digit in the unit’s place of the sum of two numbers, and the digit at unit’s place of the third number, then it is the most suitable arrangement. We will check the digit in the unit’s place of the sum of two numbers, and the digit at unit’s place of the third number in all the three arrangements to find the most suitable arrangement. A number is easier to add to another number which has 0 at the unit's place. Complete step-by-step answer: We need to find the sum of the numbers 837, 208, and 363 by suitable rearrangement. We will observe the digits at the unit's place of the three numbers. The digit at the unit's place of the number 837 is 7. The digit at unit’s place of the number 208 is 8. The digit at unit’s place of the number 363 is 3. We will check which arrangement is the most suitable. Arrangement 1: (837+208)+363 The sum of 7 and 8 is 15, with 5 at the unit’s place. Therefore, the sum of 837 and 208 will have 5 at the unit’s place. The digit at unit’s place of the number 363 is 3. Therefore, in this arrangement, we will have to add 363 and (837+208) , with the respective digits at unit’s place as 3 and 5. Arrangement 2: 837+(208+363) The sum of 8 and 3 is 11, with 1 at the unit’s place. Therefore, the sum of 208 and 363 will have 1 at the unit’s place. The sum of 208 and 363 is 571. The digit at the unit's place of the number 837 is 7. Therefore, in this arrangement, we will have to add 837 and (208+363) , with the respective digits at unit’s place as 7 and 1. Arrangement 3: (837+363)+208 The sum of 7 and 3 is 10, with 0 at the unit’s place. Therefore, the sum of 837 and 363 will have 0 at the unit’s place. The digit at unit’s place of the number 208 is 8. Therefore, in this arrangement, we will have to add 208 and (837+363) , with the respective digits at unit’s place as 8 and 0. Now, out of the three arrangements, we can observe it is easier to add 208 and (837+363) , because the digits at the unit’s place are 8 and 0 respectively. These can be added more easily as compared to other arrangements. Therefore, we will follow this arrangement. Rewriting the sum of the three numbers 837, 208, and 363, we get ⇒837+208+363=837+363+208⇒837+208+363=(837+363)+208 Adding the numbers in the parentheses, we get ⇒837+208+363=1200+208 Adding the numbers 1200 and 208, we get ⇒837+208+363=1408 Therefore, the sum of the three numbers 837, 208, and 363 is 1408. Note: Since adding 1200 and 208 is quite easy, the chosen arrangement (837+363)+208 is the most suitable one. We can verify this by checking the other arrangements. Arrangement 1: (837+208)+363 Rewriting the sum of the three numbers 837, 208, and 363, we get ⇒837+208+363=(837+208)+363 Adding the numbers in the parentheses, we get ⇒837+208+363=1045+363 We can observe that adding 1045 and 363 is not as simple as adding 1200 and 208. Therefore, arrangement 1 is not the most suitable arrangement. Arrangement 2: 837+(208+363) Rewriting the sum of the three numbers 837, 208, and 363, we get ⇒837+208+363=837+(208+363) Adding the numbers in the parentheses, we get ⇒837+208+363=837+571 We can observe that adding 837 and 571 is not as simple as adding 1200 and 208. Therefore, arrangement 2 is not the most suitable arrangement. Therefore, arrangement 3 is the most suitable arrangement.

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