Question

Find the sum of each set of numbers, as well as the size n of each set of numbers (n = number of numbers in the set). Use these exercises to practice techniques for adding numbers quickly. Try to do the problems without a calculator. Think about ways in which grouping the numbers might make them easier to add (1) (a) 25, 35, 19, 31 (i) Sum: (üi) n: (b) 101, 73, 49, 27, 24, 36 (i) Sum: (c) 25, 25, 25, 30, 30, 30, 32, 32, 32 i) Sum:

Answer 1

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