# Numbers Near 100

Before learning how to multiply two numbers near 100, you shoud first learn and feel comfortable multiplying NumbersNear

?10. This process is very similar, except that it allows you to work with larger numbers. As always, practice with numbers appropriate to each step, and you'll be amazed at how quickly and easily you'll learn to multiply numbers near 100!

## Both Numbers Above 100

To start off, we'll work with an equation in which both numbers are above 100. For this section's example, we'll multiply 103 * 105.

Instead of 10 as the "reference number", we'll be using 100. So, we start by subtracting 100 from both numbers:

103 - 100 = 3

105 - 100 = 5

Next, you're not going to add either number's difference from the opposing number from the equation. In this example, you can either add 5 to 103 or 3 to 105 (you'll get the same answer either way):

5 + 103 = 108

**or**

3 + 105 = 108

This number is then multiplied by 100 (the new reference point we're now using):

108 * 100 = 10,800

The two differences are then multiplied together:

3 * 5 = 15

Finally, you add this number to the previous answer:

10,800 + 15 = 10,815

Thus, the answer to 103 * 105 is 10,815!

As you can see, this is exactly the same process as NumbersNear?10, except that the reference number is changed.

## Both Numbers Below 100

When multiplying two numbers below 100, you'll be working with negative numbers again. This can seem more difficult with larger numbers, but that difficulty goes away with practice. We'll start with 97 * 94 as our example.

First, we subtract 100 from both numbers:

97 - 100 = -3

94 - 100 = -6

Next, one number's difference is added to the other number:

-6 + 97 = +91

**or**

-3 + 94 = +91

This number is then multiplied by 100:

91 * 100 = 9,100

Finally, the two differences are multiplied together (-3 * -6 = +18) and added to the previous answer:

9,100 + 18 = 9,118

## Numbers Above AND Below 100

Finally, we'll use 98 * 107 to demonstrate the process of multiplying one number under 100 by another number over 100.

We start by subtracting 100 from both sides:

98 - 100 = -2

107 - 100 = 7

Next, add either number's difference to the opposing number:

7 + 98 = 105

**or**

-2 + 107 = 105

Multiply this number by 100:

105 * 100 = 10,500

Remember to take the signs into consideration as you multiply the differences of the two numbers:

-2 * 7 = -14

Finally, we add this answer to the previous answer:

-14 + 10,500 = 10,486

This gives us the answer of 98 * 107 as 10,486.