# 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 × 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.

### 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.

### Exercises

1. Find the product of 128 × 122.

2. Find the product of 101 × 111.

3. Find the product of 136 × 134.