Quantitative Aptitude - SPLessons

Two Three-Digit Numbers Product

SPLessons 5 Steps, 3 Clicks
5 Steps - 3 Clicks

Two Three-Digit Numbers Product

shape Introduction

How to Quickly Calculate the Two Three-Digit Numbers Product?


In this article, we will be studying various tricks to calculate the Two Three-Digit Numbers Product.


shape Trick 1

Suppose, to calculate the product of two numbers, i.e. MNO × PQR. Then


Step 1: Multiply O and R.


Step 2: Multiply MN and MN + 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:


Condition 1– First check if ‘O + R = 10’.


Condition 2– Next check if MN and PQ are same digits, i.e. ‘MN = PQ’.


For example,

  • 563 x 567: Here, O = 3 and R = 7. This means O + R = 3 + 7 = 10. Also, MN = 56 and PQ = 56. This means MN = PQ = 5. So we can apply this TRICK here.

  • 125 x 125: Here, O = 5 and R = 5. This means O + R = 5 + 5 = 10. Also, MN = 12 and PQ = 12. This means MN = PQ = 12. So we can apply this TRICK here.

  • 132 x 137: Here, O = 2 and R = 7. This means O + R = 2 + 7 = 9 = 10. So we CANNOT apply this TRICK here.

  • 382 x 498: Here, O = 2 and R = 8. This means O + R = 2 + 8 = 10. But, MN = 38 and PQ = 49. This means MN ƒ= PQ. So we CANNOT apply this TRICK here.


Examples:

Following are some examples to understand this method.

  • 106 × 104 =?: From Step 1 we have, 6 × 4 = 24 and from Step 2 we have, 10 × (10 + 1) = 10 × (11) = 110. So the answer will be 11024.

  • 118 × 112 =?: From Step 1 we have, 8 × 2 = 16 and from Step 2 we have, 11 × (11 + 1) = 11 × (12) = 132. So the answer will be 13216.


shape Trick 2

We will understand this method using examples. We choose the base to be 100.


Example 1:

Find the product of 107 × 102 =?


Step 1: Find the difference of the numbers with respect to 100.



Step 2: Add first number with the difference of the other. We get 107 + 2 = 109.



Step 3: Multiply the result of Step 2 with 100. We get 109 × 100 = 10900.


Step 4: Multiply the differences obtained in Step 1.



We get 7 × 2 = 14.


Step 5: Add the results obtained in Step 3 and Step 4 to get the answer.


∴ The answer is 10900 + 14 = 10914.


Example 2:


Find the product of 112 × 109 =?


Step 1: Find the difference of the numbers with respect to 100.



Step 2: Add first number with the difference of the other. We get 112 + 9 = 121.



Step 3: Multiply the result of Step 2 with 100. We get 121 × 100 = 12100.


Step 4: Multiply the differences obtained in Step 1.



We get 12 × 9 = 108.


Step 5: Add the results obtained in Step 3 and Step 4 to get the answer.


∴ The answer is 12100 + 108 = 12208.


shape Exercises

1. Find the product of 128 × 122.

2. Find the product of 101 × 111.

3. Find the product of 136 × 134.


Answers:

    1. 15616

    2. 12111

    3. 18224