**Middle School Number Sense Lesson 100: Multiplying Two 2-Digit Numbers Using the FOIL Method**

This concept is the easier version of

**FOIL3by3Digit**. It can be used in many multiplication problems, but it is usually not the most efficient method to solve the problem. It showed up

**3 times**this year, with a median placement at

**question # 38**.

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Before defaulting to the FOIL (or LIOF) method, make sure there is not some other relationship between the numbers that would make the multiplication easier, like:

**How to Solve:**

**L (Last)**: Multiply the units digits together. If the product has 1 digit, write it down. If it has 2 digits, write the units digit & regroup the tens digit.**IO (Inside/Outside)**: Multiply each tens digit by the opposite number’s units digit, and add these products together. Add any regrouping from Step 1. Write the units digit of the result in front, and regroup any other digit(s).**F (First)**: Multiply the tens digits together. Add any regrouping from Step 2, and write the result in front.

**Example 1: 32 x 41 = ___**

**L**: 2 x 1 =**2**; write this down.**IO**: 2 x 4 =**8**; 3 x 1 =**3**. 8 + 3 =**11**; write the**1**in front and regroup the**1**.**F**: 3 x 4 =**12**, + the regrouped 1 =**13**. Write this in front. Your answer is**1312**.

**Example 2: 56 x 48 = ___**

**L**: 6 x 8 =**48**; write the**8**and regroup the**4**.**IO**: 6 x 4 =**24**; 5 x 8 =**40**. 24 + 40 + the regrouped 4 =**68**; write the**8**and regroup the**6**.**F**: 5 x 4 =**20**, + the regrouped 6 =**26**. Write this in front. Your answer is**2688**.

**Example 3: 63 x 28 = ___**

**L**: 3 x 8 =**24**; write the**4**and regroup the**2**.**IO**: 3 x 2 =**6**; 6 x 8 =**48**. 6 + 48 + the regrouped 2 =**56**; write the**6**and regroup the**5**.**F**: 6 x 2 =**12**, + the regrouped 5 =**17**. Write this in front. Your answer is**1764**.

**Example 4: 49 x 29 = ___**

**L**: 9 x 9 =**81**; write the**1**and regroup the**8**.**IO**: 9 x 2 =**18**; 4 x 9 =**36**. 18 + 36 + the regrouped 8 =**62**; write the**2**and regroup the**6**.**F**: 4 x 2 =**8**, + the regrouped 6 =**14**. Write this in front. Your answer is**1421**.

**Example 5: 48 x 41 = ___**

**L**: 8 x 1 =**8**; write this down.**IO**: 8 x 4 =**32**; 4 x 1 =**4**. 32 + 4 =**36**; write the**6**in front and regroup the**3**.**F**: 4 x 4 =**16**, + the regrouped 3 =**19**. Write this in front. Your answer is**1968**.

**Up Next for Middle School: SolveXRatio**