**Middle School Number Sense Lesson 95: Multiplying Two Numbers Near 100 (One Above, One Below)**

This concept is similar to, but more difficult than,

**Mult90-99**and

**Mult101-109**. It appeared

**6 times**this year in middle school, with a median placement at

**question # 64**.

The best way I can personally visualize these problems is to change them up a bit and then

**FOIL**them:

**97 x 104**becomes

**(100 – 3)(100 + 4)**

**How to Solve:**

- Figure out the distance each number is from 100:
**-3 and 4**. **F**: Start at 10,000 (100 x 100).**OI**: Add the results from Step 1 (-3 + 4 =**1**), and**add 100 times**this sum to Step 2. 10000 + 100 =**10100**.**L**: Multiply the results from Step 1 (-3 x 4 =**-12**), and add this to Step 3. 10100 – 12 =**10088**.

**Example 1: 96 x 106 = ___**

- Figure out the distance each number is from 100:
**-4 and 6**. **F**: Start at 10,000 (100 x 100).**OI**: Add the results from Step 1 (-4 + 6 =**2**), and**add 100 times**this sum to Step 2. 10000 + 200 =**10200**.**L**: Multiply the results from Step 1 (-4 x 6 =**-24**), and add this to Step 3. 10200 – 24 =**10176**.

**Example 2: 98 x 107 = ___**

- Figure out the distances:
**-2 and 7**. **F**: Start at 10000.**OI**: Add the results from Step 1 (-2 + 7 =**5**), so**add 500**to Step 2. 10000 + 500 =**10500**.**L**: Multiply the results from Step 1 (-2 x 7 =**-14**), and add this to Step 3. 10500 – 14 =**10486**.

**Example 3: 103 x 95 = ___**

- Figure out the distances:
**3 and -5**. **F**: Start at 10000.**OI**: Add the results from Step 1 (3 + -5 =**-2**), so**add -200**to Step 2. 10000 – 200 =**9800**.**L**: Multiply the results from Step 1 (3 x -5 =**-15**), and add this to Step 3. 9800 – 15 =**9785**.

**Example 4: 94 x 108 = ___**

- Figure out the distances:
**-6 and 8**. **F**: Start at 10000.**OI**: Add the results from Step 1 (-6 + 8 =**2**), so add**200**to Step 2: 10000 + 200 =**10200**.**L**: Multiply the results from Step 1 (-6 x 8 =**-48**), and add this to Step 3: 10200 – 48 =**10152**.

**Example 5: 91 x 108 = ___**

- Figure out the distances:
**-9 and 8**. **F**: Start at 10000.**OI**: Add the results from Step 1 (-9 + 8 =**-1**), so add**-100**to Step 2: 10000 – 100 =**9900**.**L**: Multiply the results from Step 1 (-9 x 8 =**-72**), and add this to Step 3: 9900 – 72 =**9828**.

**Up Next for Middle School: ProbDeckCards**