Week | Topic and action |
---|---|
Week 3 |
Example 1.
66 + 198 = 66 + 200 − 2 = 266 − 2 = 264.
Analyze: 198 → 200. The key is to think of 198 as 200, which is 2 more than 198. This is why you must subtract 2 from the sum to get the correct answer.
Example 2.
22 + 202 = 22 + 200 + 2 = 222 + 2 = 224.
Example 3.
683 − 397 = 683 − 400 + 3 = 283 + 3 = 286.
Analyze: 397 → 400. The key is to think of 397 as 400, which is 3 more than 397. This is why you must add 3 to the sum to get the correct answer.
Example 4.
363 − 302 = 363 − 300 − 2 = 63 − 2 = 61.
a + b = b + a
(a + b) + c = a + (b + c)
Example 5.
45 + 68 + 55 = (45 + 55) + 68 = 100 + 68 = 168.
Analyze: by using commutative property and associative property, group 45 and 55 together.
Example 6
22 + 63 + 78 + 37 + 56 = (22 + 78) + (63 + 37) + 56 = 100 + 100 + 56 = 256.
Example 7.
237 − 26 − 137 = (237 − 137) − 26 = 100 − 26 = 74.
Analyze: The key is to switch the positions of the two numbers 26 and 137.
Example 8.
567 + 123 − 367 = (567 − 367) + 123 = 200 + 123 = 323.
Analyze: The key is to switch the positions of the two numbers 123 and 367.
Example 9.
123498 − 123466 = 98 − 66 = 32.
Analyze: Observing the two numbers. Only the last two digits are different.
Example 10.
2 + 92 + 992 + 9992 + 99992
= (10 − 8) + (100 − 8) + (1000 − 8) + (10000 − 8) + (100000 − 8)
= 111110 − 5 × 8
= 111070
Example 11.
24 − 22 + 20 − 18 + 16 − 14 + 12 − 10 + 8 − 6
= (24 − 22) + (20 − 18) + (16 − 14) + (12 − 10) + (8 − 6)
= 2 × 5 = 10.
Example 12.
69 + 70 + 71 + 72 + 73 + 74
= (70 − 1) + 70 + (70 + 1) + (70 + 2) + (70 + 3) + (70 + 4)
= 70 × 5 − 1 + 1 + 2 + 3 + 4 = 350 + 9 = 359