**Middle School Number Sense Lesson 24: Multiplying Two Numbers Just above 100**

This skill requires a bit of imagination, but once you figure it out, it takes just a few seconds to solve these types of problems. They appeared

**11 times**this year, most often at

**question 29**.

**Number Dojo Level: 113**

When you see these problems,

**imagine**each number is made up of two parts:

- 100
- A small number added to the 100

This will be important in coming up with a quick solution. It taps into our FOILing skills (like I explained in the

**DiffSquares1**post). So

**103 x 109**becomes

**(100 + 3)(100 + 9)**.

Don't worry about the FOIL steps, because this concept is a couple of steps quicker. Here's how you solve these problems:

- Think: "How far above 100 are each of these numbers?" This refers back to the small numbers in #2 in the
**imagine**section above. If both numbers are < 110, we're simply working with the units digits. - Multiply those two small numbers together & write their product down as 2 digits. (If their product exceeds two digits, write the last 2 digits and regroup the first).
- Add the first (100+) number to the second small number (and any regrouping), and write this sum in front of the product from step 2.

**It's actually much easier than it looks. Let's work through a few examples.**

*Confused? Me too.***Example 1: 106 x 107**

- Write down the product of the units digits: 6 x 7 =
**42**. - Add the first number (
**106**) and the units digit of the second number (**7**). 106 + 7 =**113**. Write this in front. Your answer is**11342**. (I told you it's easier than it looks!)

**Example 2: 108 x 103**

- Write down the product of the units digits: 8 x 3 =
**24**. - Add the first number (
**108**) and the units digit of the second (**3**). 108 + 3 =**111**; write this in front. The answer is**11124**.

**Example 3: 104 x 109**

- Multiply the units digits: 4 x 9 =
**36**; write this down. - 104 + 9 =
**113**; write this in front. The answer is**11336**.

**Example 4: 111 x 105**

- Multiply
**11 x 5**(the distance above 100 for each number) to get**55**; write this down. - 111 + 5 =
**116**; write this in front. The answer is**11655**.

**Example 5: 102 x 118**

- 2 x 18 =
**36**; write this down. - 102 + 18 =
**120**; write this in front. The answer is**12036**.

**Example 6: 101 x 104**

- 1 x 4 = 4; write down
**04**(this step always has to produce a 2-digit answer). - 101 + 4 =
**105**; write this in front. The answer is**10504**.

**Example 7: 109 x 112**

- 9 x 12 = 108; write down
**08**and regroup the 1. - 109 + 12 (+ the regrouped 1) =
**122**; write this in front. The answer is**12208**.

**Here's a free worksheet to help you practice Mult101-109:**

mult101-109.pdf |

**And a video.**

Up Next for Middle School: Mult90-99

Up Next for Middle School: Mult90-99