Quantitative Aptitude - SPLessons

Multiplying Two 2-Digit Numbers

SPLessons 5 Steps, 3 Clicks
5 Steps - 3 Clicks

Multiplying Two 2-Digit Numbers

shape Introduction

Multiplying Two 2-Digit Numbers – Quick Calculation Tricks
In this article, we will be looking at various tricks to calculate the Product of Two 2-Digit Numbers.


shape TRICK #1

Case: The ten’s digit of the two 2-digit numbers is 1. Example: 14*15; 12*17; 14*17.

Example 1: Find 14×17?


Step 1:
Add the first number to the last digit of the second number:
14 + 7 = 21


Step 2: Multiply the result by 10:
21 x 10 =210


Step 3: Multiply the last digits of both numbers together:
4 x 7 = 28


Step 3: Add results of Step 2 & Step 3
210 + 28 = 238


Example 2: Find 16×19?


Step 1:
Add the first number to the last digit of the second number:
16 + 9 = 25


Step 2: Multiply the result by 10:
25 x 10 = 250


Step 3: Multiply the last digits of both numbers together:
6 x 9 = 54

Step 4: Add results of Step 2 & Step 3
250 + 54 = 304


shape TRICK #2

Suppose we want to calculate the product of two numbers, i.e. MN × PQ. Then


Step 1: Multiply N and Q.


Step 2: Multiply M and M + 1.


Step 3: Arrange the products of Step 1 and Step 2 from RHS to LHS to get the answer.


This trick is applicable only when the following both conditions are satisfied:



For example,


  • 56 × 54 : Here, N = 6 and Q = 4. This means N + Q = 6 + 4 = 10. Also, M = 5 and P = 5.
    This means M = P = 5. So we can apply this TRICK here.

  • 41 × 49 : Here, N = 1 and Q = 9.
    This means N + Q = 1 + 9 = 10. Also, M = 4 and P = 4.
    This means M = P = 4. So we can apply this TRICK here.

  • 32 × 37 : Here, N = 2 and Q = 7.
    This means N + Q = 7 + 2 = 9 6= 10. So we CANNOT apply this TRICK here.

  • 82 × 98 : Here, N = 2 and Q = 8.
    This means N + Q = 2 + 8 = 10. But, M = 8 and P = 9.
    This means M \(\neq\) P. So we CANNOT apply this TRICK here.


Let’s see some examples to understand this method.


  • 56×54 =?: From Step 1 we have, 6×4 = 24 and from Step 2 we have, 5×(5+1) = 5×(6) = 30. So the answer will be 3024.

  • 78×72 =?: From Step 1 we have, 8×2 = 16 and from Step 2 we have, 7×(7+1) = 7×(8) = 56. So the answer will be 5616.


shape TRICK #3

We will understand this method using examples.

Example 1: 77 × 78 =?


Step 1:

    Multiply units digit (77 and 78) of both the numbers. We get 7 × 8 = 56. Keep only the units digit ‘6’ (i.e. 56) of this product and carry over the tens digit (i.e. 56) to the next step.


Step 2:

    Multiply the similar color digits as shown 77 × 78 and add there products with the previous step carry, if any. In this case we have, (7 × 7) + (7 × 8) + 5 = 110. Again, keep only the units digit ‘0’ (i.e. 110) of this product and carry over the leftover digits (i.e. 110) to the next step.


Step 3:

    Multiply the tens digit of the numbers again and add the carry from previous Step, if any. In this case 77 × 78. So 7 × 7 + 11 = 49 + 11 = 60.


Step 4:

    Arrange the products obtained from previous Steps from RHS to LHS. So our answer will be 6006.


Example 2: 36 × 54 =?


Step 1:

    Multiply units digit (36 and 54) of both the numbers. We get 6 ×4 = 24. Keep only the units digit ‘4’ (i.e. 24) of this product and carry over the tens digit (i.e. 24) to the next step.


Step 2:

    Multiply the similar color digits as shown 36 × 54 and add there products with the previous step carry, if any. In this case we have, (6 × 5) + (3 × 4) + 2 = 44. Again, keep only the units digit ‘4’ (i.e. 44) of this product and carry over the leftover digits (i.e. 44) to the next step.


Step 3:

    Multiply the tens digit of the numbers again and add the carry from previous Step, if any. In this case 36 × 54. So 3 × 5 + 4 = 15 + 4 = 19.


Step 4:

    Arrange the products obtained from previous Steps from RHS to LHS. So our answer will be 1944.


shape Exercises

1. Find the product of 28 × 76 .

2. Find the product of 31 × 39 .

3. Find the product of 99 × 55 .

Answers:


    1. 1568

    2. 1209

    3. 5445