Page 186 - Start Up Mathematics_4

Predicting patterns

We can follow some simple steps to predict patterns. Consider the numbers 2, 6, 7, 21, 22.
Let’s see how we can predict the pattern in them.

Step 1: Add or subtract the numbers to predict the pattern.
+4 +1 +14 +1
2 6 7 21 22 — Here, (+4) (+1) (+14) (+1) does not form a pattern.

Step 2: Multiply or divide the numbers.
×3 +1 ×3 +1
2 6 7 21 22 — Here, (×3) (+1) forms a pattern.

Thus by seeing the relationship between 3 or 4 consecutive numbers in a sequence, we can
predict its pattern.

Casting out Nine

By repeatedly adding the digits of any given number, we can get a single digit. It is called
Check Digit.
Consider the following examples.

6 3 9 5 → 6 + 3 + 9 + 5 = 23 → 2 + 3 = 5 check digit

1 2 5 9 → 1 + 2 + 5 + 9 = 17 → 1 + 7 = 8 check digit
Now, remove 9 from 6395 and 1259. The numbers will be 635 and 125. Add the digits again.

6 3 5 → 6 + 3 + 5 = 14 → 1 + 4 = 5 check digit

1 2 5 → 1 + 2 + 5 = 8 → check digit
Thus, we find that removing 9 from a number does not change its check digit. So, we can
assign the value zero to 9 in a number and CAST IT OUT of that number.

Casting out nine helps to check if an addition answer is correct or not. The rule for checking
is as follows.

If you add a set of numbers, the check digit of their sum will be equal to the check digit of
the sum of the check digits of each number.
Example 8: Cast out nine and check if the sum of 3,96,824; 1,29,148 and 4,97,214 is 96,186
or not.

Solution: Numbers after Check digits of the number
casting out nine
3 6 8 2 4 5
1 2 1 4 8 7
+ 4 7 2 1 4 + 9

9 6 1 8 6 21 → 2 + 1 = 3

9 + 6 + 1 + 8 + 6 = 30 → 3 + 0 = 3
Since the check digits are same, the sum is correct.

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