It is a presentation for multiplying two to three digits in short cut method

1. MATHEMATICS ENHANCEMENT
in NUMERACY THROUGH
ACTIVE LEARNING (MENTAL)
MATH
Dr. Feliculo U. Japona, Jr.,PhD
Binuangan National High School

2. Multiplication of numbers
Case 1 : Multiplication 2 digit by 2 digit
Example 1. Find the product of 24 and 46.
2
24
x 26
144 partial product
48
624 product

3. Shortcut method (Pattern 1)
Case 1 : Multiplication 2 digit by 2 digit
Example 1. Find the product of 24 and 46.
2 o o
24 o o 4 X 6 = 24 carry over
x 2 26 o o
624 o o 2x6 = 12 , 2x 4 = 8 => 12 + 8 = 20 + 2 = 22
o o carry over
o o 2x 2 = 4 + 2 = 6

4. Example 2. Find the product of 57 and 86.
4 o o
57 o o 7 X 6 = 42 carry over
x 9 86 o o
4902 o o 5x6 = 30 , 7x 8 = 56 => 30 +56 = 86 + 4 = 90
o o carry over
o o 5x 8 = 40 + 9 = 49

5. Example 3. Find the product of 34 and 98.
3 o o
34 o o 4 X 8 = 32 carry over
x 6 98 o o
3332 o o 3x8 = 24 , 4x 9 = 36 => 24 +36 = 60 + 3 = 63
o o carry over
o o 3x 9 = 27 + 6 = 33

6. Multiplying 3 digit by 3 digit
Example 1. Multiply 234 by 476
Solution : 2 2
2 2 234
1 1 x 476
1404
1638 partial product
936
111384 final product

7. Shortcut method (Pattern 2)
Case 2 : Multiplication 3 digit by 3 digit
Example 1. Find the product of 234 and 476.
5 4 2 o o o o o o 3 x 6 = 18 carry over
234 o o o 4 X 6 = 24 o o o 4 x 7 = 28 =>18+28=46 +2 = 48
x 3 476 o o o 2 x 6 =12 , 4 x 4 =16 , 3 x 7 = 21 carry over
111384 o o o 12 + 16 +21 = 49 + 4 = 53
o o o 2 x 7 = 14 carry over o o o carry over
o o o 3x 4 = 12=> 14+12= 26 +5 = 31 o o o 2 x 4 = 8 + 3 =11

8. Example 2. Find the product of 945 and 578.
13 7 4 o o o o o o 4 x 8 = 32 carry over
945 o o o 5 X 8 = 40 o o o 5 x 7 = 35 =>32+35=67 +4 = 71
x 9 578 o o o 9 x 8 =72 , 5 x 5 =25 , 4 x 7 = 28 carry over
546210 o o o 72 + 25 +28 = 125 + 7 = 132
o o o 9 x 7 = 63 carry over o o o carry over
o o o 4 x 5 = 20=> 63+20= 83 +13 = 96 o o o 9 x 5 = 45 + 9 =54

9. Example 3. Find the product of 632 and 97.
7 4 1 o o o o o o 2 x 9 = 18 carry over
632 o o o 2 X 7 = 14 o o o 3 x 7 = 21 =>18+21=39 +1 = 40
x 6 097 o o o 6 x 7 =42 , 0 x 2 =0 , 3 x 9 = 27 carry over
61304 o o o 42 + 0 + 27 = 69 + 4 = 73
o o o 6 x 9 = 54 carry over o o o carry over
o o o 0 x 3 = 0=> 54+0= 54 +7 = 61 o o o 0 x 6 = 0 + 6 =6

10. PATTERN
Case 1: 2 digits by 2 digits
o o o o o o
o o o o o o
1 2 1
Case 2: 3 digits by 3 digits
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
1 2 3 2 1

11. Case 3: 4 digits by 4 digits
o o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o o
1 2 3 4
o o o o o o o o o o o o
o o o o o o o o o o o o
3 2 1

12. Squaring 2 digit number
Example 1: What is 26 2
?
Step 1. Square the ten digit number : 2 x 2 = 04
Step 2. Square the one digit number: 6 x 6 = 36
26 2
0436
24
676
Step 3: Multiply tens digits by one digits then double it. 2x6=12 x2 =24
Place under 43 then add. Final answer comes in.

13. Example 2: What is 94 2 ?
Step 1. Square the ten digit number : 9 x 9 = 81
Step 2. Square the one digit number: 4 x 4 = 16
94 2
8116
72
8836
Step 3: Multiply tens digits by one digits then double it. 9x4=36 x2 =72
Place under 11 then add. Final answer comes in.

14. Squaring 3 digit number
Example 1: What is 2672 ?
Step 1 : Square the hundred digits: 2 x 2 = 04
Step 2 : Square the ten digits : 6 x 6 = 36
Step 3 : Square the one digits : 7 x 7 = 49
Step 4 : Multiply the one digits by tens digit then double:
6 x7 = 42 x 2 = 84
Step 5:Multiply the ten digits by hundred digits then double:
2 x 6 = 12 x 2 = 24

15. Arrange them together as shown below:
2672
043649
2484
28
71289
Step 6: Multiply the hundred digits and one digits then double:
2 x 7 = 14 x 2 = 28 place under hundred digits then add.

16. Example 2: What is 9372 ?
Step 1 : Square the hundred digits: 9 x 9 = 81
Step 2 : Square the ten digits : 3 x 3 = 09
Step 3 : Square the one digits : 7 x 7 = 49
Step 4 : Multiply the one digits by tens digit then double:
7 x3 = 21 x 2 = 42
Step 5:Multiply the ten digits by hundred digits then double:
3 x 9 = 27 x 2 = 54

17. Arrange them together as shown below:
9372
810949
5442
126
877969
Step 6: Multiply the hundred digits and one digits then double:
9 x 7 = 63 x 2 = 126 place under hundred digits then add.

18. Multiplying Polynomials
Example 1: Multiply 3x + 2 by 4x-9
Use 1 2 1 pattern:
3x + 2 o o o o o o
4x - 9 o o o o o o
12𝑥2
-19x -18 2(-9) 3x(-9)+4x(2) 3x(4x)
-27x+8x 12𝑥2
-19x

19. Example 2: Multiply 8x - 3 by 5x +10
Use 1 2 1 pattern:
8x - 3 o o o o o o
5x +10 o o o o o o
40𝑥2 +25x -30 -3(10) 8x(10)+5x(-3) 8x(5x)
40x-15x 40𝑥2
25x

20. Example 3: Multiply 4𝑥2
-5x -2 by 3𝑥2
+6x + 1
Use 1 2 3 2 1 pattern:
4𝑥2
-5x - 2 o o o o o o o o o
3𝑥2
+6x + 1 o o o o o o o o o
12𝑥4
+9𝑥3
-32𝑥2
-17x -2 -2(1) (-5x)(1)+6x(-2) 4𝑥2
(1)+ 3𝑥2
(-2) +(-5x)(6x)
-5x-12x 4𝑥2
−6𝑥2
- 30𝑥2
-17x - 32𝑥2
o o o o o o
o o o o o o
4𝑥2
(6x)+ 3𝑥2
(-5x) 4𝑥2
( 3𝑥2
)
24𝑥3
− 15 𝑥3
12𝑥4
9𝑥3

21. Example 4: Multiply 2𝑥2
+3x +5 by 𝑥2
-x + 1
Use 1 2 3 2 1 pattern:
2𝑥2
+3x + 5 o o o o o o o o o
𝑥2
- x + 1 o o o o o o o o o
12𝑥4
+9𝑥3
-32𝑥2
-17x -2 -2(1) (-5x)(1)+6x(-2) 4𝑥2
(1)+ 3𝑥2
(-2) +(-5x)(6x)
-5x-12x 4𝑥2
−6𝑥2
- 30𝑥2
-17x - 32𝑥2
o o o o o o
o o o o o o
4𝑥2
(6x)+ 3𝑥2
(-5x) 4𝑥2
( 3𝑥2
)
24𝑥3
− 15 𝑥3
12𝑥4
9𝑥3