**Middle School Number Sense Lesson 31: Multiplying by 111**

About 3 months ago, we began this journey (getting a daily dose of Number Dojo) with

**Mult11**. That concept is usually one of the first ones taught, and this one is its older sibling. It appeared

**14 times**this year, but on average it was much later in the test than last year. Last year (for the most part) it was between questions 13 & 19. This year, for some reason, it was in the 20s 3 times, in the 30s once, in the 40s 3 times, in the 60s 6 times, and in the 70s once. The average spot was at

**question # 50**.

**Number Dojo Level: 89**

If you haven't learned

**Mult11**, or if you've forgotten how to do it, you may want to review it now by clicking on the link (embedded in its name). This concept is only slightly harder. First I will demonstrate multiplying 111 by a 3-digit number, and then I will show how to solve these with a larger or smaller number.

**How it Works:**

- Write down the units digit.
- Add the units & tens digits and write down the sum in front if less than 10. (If the sum has 2 digits, write down its units digit and regroup the 1).
- Add triples of neighboring digits--so the units, tens, & hundreds (plus the regrouped 1, if any). Write down the sum in front if <10. (If the sum has 2 digits, write down its units digit and regroup its tens digit).
- Add the first two digits (plus the regrouped number, if any). Write down the sum if <10. (If the sum has 2 digits, write down its units digit and regroup its tens digit).
- Write down the first digit (plus the regrouped number, if any).

**Example 1: 111 x 314**

- Write down the units digit:
**4**. - Add the units digit (4) & the tens digit (1) to get
**5**; write this down in front. - Add the three neighboring digits: 4 + 1 + 3 =
**8**; write this down in front. - Add the tens digit (1) & the hundreds digit (3) to get
**4**; write this down in front. - Write down the hundreds digit in front:
**3**. The answer is**34854**.

**Example 2: 513 x 111**

- Write down the units digit:
**3**. - Add the units digit (3) & the tens digit (1) to get
**4**; write this down. - Add the three neighboring digits: 3 + 1 + 5 =
**9**; write this down. - Add the tens digit (1) & the hundreds digit (5) to get
**6**; write this down. - Write down the hundreds digit:
**5**. The answer is**56943**.

**Example 3 (with regrouping): 111 x 742**

- Write down the units digit:
**2**. - Add the units digit (2) & the tens digit (4) to get
**6**; write this down. - Add the three neighboring digits: 2 + 4 + 7 = 13. Write down the
**3**and regroup the 1. - Add the tens digit (4) & the hundreds digit (7), & the regrouped 1 to get 12. Write down the
**2**and regroup the 1. - Add the hundreds digit (7) and the regrouped 1 to get
**8**; write this down. The answer is**82362**.

**Example 4 (4-digit number): 1776 x 111**

- Write down the units digit:
**6**. - Add the units digit (6) & the tens digit (7) to get 13; write down the
**3**and regroup the 1. - Add triples of neighboring digits: 6 + 7 + 7 = 20, plus the regrouped 1 is 21. Write down the
**1**and regroup the 2. - 7 + 7 + 1 (plus the regrouped 2) = 17; write the
**7**and regroup the 1. - Add the first 2 digits (7 + 1) & the regrouped 1 to get
**9**; write this down. - Write down the first digit:
**1**. The answer is**197136**.

**Example 5 (2-digit number): 86 x 111**

- Write down the units digit:
**6**. - Add the two digits: 8 + 6 = 14; write down the
**4**and regroup the 1. - Repeat since there is no triple of neighboring digits. 8 + 6 (plus the regrouped 1) = 15; write the
**5**and regroup the 1. - Add the first digit (8) and the regrouped 1 to get
**9**; write this down. The answer is**9546**.

**This one takes practice! Here's a free worksheet to help you practice Mult111:**

mult111.pdf |

**And a video.**

Up Next for Middle School: Reciprocal

Up Next for Middle School: Reciprocal