For the past few weeks we have been looking at multiplication methods, so this week let us look at some ways that help us add mentally. Here also the zero numbers play a vital role in making our addition easier.
Addition by completing to ten From the above circle, we can see the five pairs of numbers that add up to 10:
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
So we look out for numbers that total up to 10 while adding other numbers.
For example, if you come across 16 + 4, you club the 6 and 4 (= 10) and get the answer 20 in your mind.
As soon as you see 37 and 23, your mind must combine the 7 and 3 to make 10 and then add the 30 and 20. The total becomes 60, all in the mind.
If we come across 16 + 23 + 24 + 17, we combine 16 and 24 to make 40 and then 23 and 17 to make 40 and get the final answer: 80.
Try the following:
a. 27 + 23
b. 42 + 28
c. 54 + 16
d. 49 + 21
e. 45 + 35
f. 72 + 18
g. 38 + 22
h. 35 + 35
i. 19 + 11 + 12 + 8
j. 34 + 35 + 16 + 5
Addition by finding the deficiency
The next method is to identify numbers which are close to, particularly less than, the numbers ending in zero. For example, 28 is 2 less than 30, 49 is 1 less than 50 and so on. After finding the deficiency, we can complete the whole and make our mental addition easy.
Example: 58 +4
As soon as you see 58 your mind should tell you that you need 2 to make 60, so split 4 as 2 + 2.
• 58 + 2 = 60
• 60 + 2 = 62 is the answer
29 + 7 +1 + 4
• First combine 29 and 1 to complete 30
• Looking at the remaining numbers we know 7 and 3 make 10 so split 4 as 3 and 1
• 7+3+1= 10 +1 = 11
• 30 +11= 41 is the answer
6 + 7 + 4
• You will see that 6 and 4 make 10.
• Add the 7 last to get 6 + 7 + 4 = 17
Now you can try these:
a. 3 + 2 + 8
b. 9 + 8 + 1
c. 7 + 2 + 4 + 3
d. 4 + 5 + 5 + 7
e. 8 + 9 + 2
f. 7 + 6 + 2 + 4
g. 8 + 8 + 3 + 2
h. 7 + 6 + 3 + 4
i. 4 + 7 + 4 + 2
j. 6 + 9 + 2 + 2
k. 7 + 5 + 1 + 2
l. 3 + 5 + 4 + 3
3 + 6 + 2 + 5
• 3, 2 and 5 make 10 so add these first and then add the 6
• 3 + 2 + 5 = 10 + 6 = 16
• In this problem we have combined 3 numbers to get 10.
Now I am going to give you a task! It is to find 3 numbers that make a total of 10. For example, 1+2+7.There are 7 more combinations of numbers, without using 0, but you can use the same number more than once. Find out!