# Two Three-Digit Numbers Product

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# Two Three-Digit Numbers Product

### 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.

### Trick 1

Suppose, to calculate the product of two numbers, i.e. MNO Ã— 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 â€˜O + R = 10â€™.

Condition 2– Next check if MN and PQ are same digits, i.e. â€˜MN = PQâ€™.

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 Æ’= PQ. So we CANNOT apply this TRICK here.

Examples:

Following are some examples to understand this method.

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

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

### Trick 2

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

Example 1:

Find the product of 107 Ã— 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 Ã— 100 = 10900.

Step 4: Multiply the differences obtained in Step 1.

We get 7 Ã— 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 Ã— 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 Ã— 100 = 12100.

Step 4: Multiply the differences obtained in Step 1.

We get 12 Ã— 9 = 108.

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

∴ The answer is 12100 + 108 = 12208.

### Exercises

1. Find the product of 128 Ã— 122.

2. Find the product of 101 Ã— 111.

3. Find the product of 136 Ã— 134.

1. 15616

2. 12111

3. 18224