By Ike Prudente
Addition with zeroes is very simple so to simplify addition we must create numbers with zeroes.
1)Add number pairs or groups totalling to ten or multiples of ten first
Example 1.1: 3 + 4 + 6 + 8 + 5 + 9 =
| 3 + 4 + 6 + 8 + 5 + 9 | |
| Add 4 and 6 first to get 10 | = 3 + (4 + 6 ) + 8 + 5 + 9 = 3 + 10 + 8 + 5 + 9 |
| Next we add 3, 8 and 9 to get 20 for a total of 30 | = 10 + ( 3 + 8 + 9 ) + 5 = (10 + 20) + 5 = 30 + 5 |
| Only the 5 remains to be added so we have a total of 35. | = 35 |
Example 1.2: 4 + 67 + 276 + 20 =
| 4 + 67 + 276 + 20 | |
| Add 4 to 276 first to get 280 | = (4+276) + 67 + 20 = 280 + 67 + 20 |
| Then add the 20 to get 300 | = (280 + 20) + 67 = 300 + 67 |
| Finally add the 67 to get 367 | = 367 |
2) Mentally create zeroes by transferring
Example 1.3: 34 + 56 =
| 34 + 56 | |
| Mentally transfer 4 from 34 to 56 | = 30 + (4 + 56) = 30 + 60 |
| Addition then become a simple 30 + 60 exercise. | = 90 |
Example 1.4: 65 + 97 =
| 65 + 97 | |
| Mentally transfer 3 from 65 to 97 to make it 100. | = 62 + (3 + 97) = 62 + 100 |
| 65 becomes 62, so the answer is 162. | = 162 |
Example 1.5: 137 + 245 + 489 =
| 137 + 245 + 489 = | |
| Transfer 11 from 137 to 489 to make it 500. | = (137 – 11) + (11+489) + 245= (137 – 11) + 500 + 245 |
| Transfer 5 from 137 to 245 to make it 250. | = (137 – 11 – 5 ) + 500 + (245 + 5)= (137 – 11 – 5 ) + 500 + 250 |
| Then we have 500 + 250 = 750 | = (137 – 11 – 5 ) + 750 |
| Finally we add 121 (137-11-5) to 750 to get 871. | = 121 + 750= 871 |
3) Sometimes it is easier to add a round number first before deducting the excess.
Example 1.6 376 + 995 =
| 376 + 995 | |
| Add 1000 to 376 to get 1376 | = 376 + (1000 – 5)= 376 + 1000 – 5
= (376 + 1000 ) – 5 = 1376 – 5 |
| Deduct 5 which is the excess of 1000 from 995 to get1371 | = 1371 |
Why it works.
This is not rocket science, but in case you are wondering, we are just using the associative and commutative properties of addition.
Exercises
a) 2 + 5 + 4 + 8 + 6 =
b) 1 + 6 + 9 + 4 + 7 =
c) 5 + 6 + 7 + 8 + 4 =
d) 8 + 4 + 9 + 8 + 3 =
e) 86 + 98 =
f) 989 + 278 =
g) 24 + 67 + 66 =
h) 287 + 471 + 313 =
i) 734 + 40 + 125 + 26 =
j) 999,967 + 666,699 =
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