**Elementary School Number Sense Lesson 11: Multiplying by 11 (variation)**

Today's lesson builds upon the

**Mult11**concept, which was our very first published lesson almost a year ago. It has appeared

**3 times**so far on this year's tests, with a median placement at

**question # 29**.

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These problems involve manipulating the number 11, but they come in a few different forms:

- using a multiple of 11 (22, 33, 44, etc.),
- dividing instead of multiplying, and/or
- including decimals

In each case, we will use some combination of our skills to solve the problem.

**Example 1: 22 x 36 = ___**

- Use
**Double/Half**to change this to**11 x 72** - 11 x 72 =
**792**

**Example 2: 44 x 13 = ___**

- Use
**Double/Half**twice to change this to**22 x 26**and then to**11 x 52** - 11 x 52 =
**572**

**Example 3: 187 ÷ 11 = ___**

- Try to recognize a pattern in these numbers: what "neighbors", when added together, equal the 8 in the middle? They're easily found at the beginning and end of the 3-digit number: 1 and 7.
- The answer is
**17**

**Example 4: 55 x 38 = ___**

- Use
**Double/Half**to change this to**110 x 19** - Write the
**0**, and now multiply**11 x 19** - 11 x 19 =
**209**, and write this in front. - The answer is
**2090**

**Example 5: 1.1 x 3.15 = ___ (decimal)**

- Notice the number 11 hiding in the
**1.1**; ignore both numbers for now and multiply**11 x 315** - 11 x 315 =
**3465** - There are 3 decimal places in the question, so there will be 3 in the answer. The answer is
**3.465**

**Here's a free worksheet to help you practice Mult11var:**

mult11var.pdf |

**Up Next for Elementary School: Ratio**