Find the value of the following expression:
3845 × 5 × 782 + 769 × 25 × 218
3845 × 5 × 782 + 769 × 25 × 218
In this question, we have to simplify some of the terms in the given expression so that the calculation becomes simpler:
Notice that we can split 25 into two 5s, so that the resulting expression gives 3845, which can then be grouped together:
3845 × 5 × 782 + 769 × 25 × 218
= 3845 × 5 × 782 + 769 × (5 × 5) × 218
= 3845 × 5 × 782 + 3845 × 5 × 218
= 3845 × 5 × (782 + 218)
[As per distributive law, a × ( b + c) = (a × b) + (a × c)]
= 19225 × 1000 = 19225000
This is the required answer.
P.S. A useful approach is to these problems is to take approximate numbers. If you notice, the largest number here is 3845, rounded we get 3800. We can approximate 769 as 750 and multiply a 5 to obtain 3750. Since these numbers are near to each other, there is a possibility that they would give the same number. Try experimenting with similar large numbers.
In this question, we have to simplify some of the terms in the given expression so that the calculation becomes simpler:
Notice that we can split 25 into two 5s, so that the resulting expression gives 3845, which can then be grouped together:
3845 × 5 × 782 + 769 × 25 × 218
= 3845 × 5 × 782 + 769 × (5 × 5) × 218
= 3845 × 5 × 782 + 3845 × 5 × 218
= 3845 × 5 × (782 + 218)
[As per distributive law, a × ( b + c) = (a × b) + (a × c)]
= 19225 × 1000 = 19225000
This is the required answer.
P.S. A useful approach is to these problems is to take approximate numbers. If you notice, the largest number here is 3845, rounded we get 3800. We can approximate 769 as 750 and multiply a 5 to obtain 3750. Since these numbers are near to each other, there is a possibility that they would give the same number. Try experimenting with similar large numbers.
