Page 166 - Math_Genius_V1.0_C4_Flipbook

E:\Working\Focus_Learning\Math_Genius_4_(25-10-2023)\Open_Files\Chap-09
\\December 6, 2023 11:06 AM Bharat Arora P-6 Reader _________________________ Date: ___________________74

Patterns in Multiplication

Observe the pattern in the following multiplications.

1. 1 × 1 = 1 2. 9 × 1 = 9
11 × 11 = 121 9 × 11 = 99

111 × 111 = 12321 9 × 111 = 999
1111 × 1111 = 1234321 9 × 1111 = 9999

Patterns Based on the Multiples of 9

Multiply any number by 9, the sum of all the digits of the product is always 9.

1. Multiple of 9 Product Sum of all digits of the product
11 × 9 99 9 + 9 = 18, 1 + 8 = 9

21 × 9 189 1+ 8 + 9 = 18, 1+ 8 = 9

111 × 9 999 9 + 9 + 9 = 27, 2 + 7 = 9

2. 1 2 3 4 5 6 7 9 × 9 = 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 9 × 18 = 2 2 2 2 2 2 2 2 2
Remember
1 2 3 4 5 6 7 9 × 27 = 3 3 3 3 3 3 3 3 3 If the sum of all digits of a number

1 2 3 4 5 6 7 9 × 36 = 4 4 4 4 4 4 4 4 4 is 9 or divisible by 9, then the
1 2 3 4 5 6 7 9 × 45 = 5 5 5 5 5 5 5 5 5 number is called a multiple of 9.

casting out 9

Let us consider the number 952632. It is a multiple of 9 as the sum of its digit = 9
+ 5 + 2 + 6 + 3 + 2 = 27 is a multiple of 9 (2 + 7 = 9), then

952632 952632 522 is also a multiple of 9 (As, 5 + 2 + 2 = 9).
Thus, any number or combination of digits in that number that add to 9 can be

cast out from the given number. Then the
sum of the number's remaining digits is Quick Check

also a multiple of 9. State whether the following numbers
are multiples of 9, by casting out 9.
Patterns in Division
1. 235897 2. 6810453
Look at the following patterns in division.

1. 6 ÷ 2 = 3 2. 10 ÷ 5 = 2

60 ÷ 2 = 30 100 ÷ 5 = 20
600 ÷ 2 = 300 1000 ÷ 5 = 200
6000 ÷ 2 = 3000 10000 ÷ 5 = 2000
60000 ÷ 2 = 30000 100000 ÷ 5 = 20000

164 Mathematics-4