We have to add numbers without a calculator.
1) 25, 35, 19, 31
We can group them by the last digit, so they are easy to add:
25 + 35 = 20 + 30 + 5 +5 = 50 + 10 = 60
19 + 31 = 10 + 30 + 9 +1 = 40 + 10 = 50
Then, 60 + 50 = 110
numbers in the set n = 4
Sum = 110
2) 101, 73, 49, 27, 24, 36
We can group them again by the last digit (adding 10, like the previous example).
We can substract the last digit from one number and add it to the other one. The result will be the same, but they will become easier to add.
101 + 49 = 100+50 = 150
73 + 27 = 70 + 30 = 100
24 + 36 = 20 + 40 = 60
150 + 100 + 60 = 250 + 60 = 310
numbers in the set n = 6
Sum = 310
3) 25, 25, 25, 30, 30, 30, 32, 32, 32
In this case we have 3 times the same numbers, so we can add the three different numbers and then multiply the total by 3.
We can use the properties of the multiplication to simplify the product (we will use the distributive property)
25 + 30 + 32 = 27 + 30 + 30 = 87
87 * 3 = 80*3 + 7*3 = 240 + 21 = 261
numbers in the set n = 9
Sum = 261
