**Middle School Number Sense Lesson 70: Multiplying by 101 (variation)**

I'm not sure why this particular concept shows up so late on a number sense test, but it is one of the quicker ones to master and to calculate. It appeared

**7 times**on last year's tests, with a median placement at

**question # 69**.

**Please Like our Facebook Page (**

**https://www.facebook.com/numberdojo/**

**) if you want to see new posts on your wall. I will reward you with a free concept index or flashcard file of your choice. Thank you!**

**Number Dojo Level: 101**

Multiplying by 101 (when there are more than 2 digits) requires 3 easy steps. The best way to solidify this process is to look at it the traditional way. Let's try:

**314**

x 101

--------

x 101

--------

**314**, and the second row will be

**000**, but staggered like this:

**314**

x 101

--------

314

000

314

--------

x 101

--------

314

000

314

--------

**31714**. Notice that:

- The first two digits of the answer are the
**first two digits**of the original number, - The third digit of the answer is the
**sum of the first and last digits**of the original number, and - The last two digits of the answer are the
**last two digits**of the original number.

**How to Solve:**

- Write down the
**last 2 digits**of the 3-digit number. - Write the
**sum of the 1st & 3rd digits**, in front (remember the regrouping). - Write the
**first 2 digits**of the original number in front of that.

**Example 1: 101 x 422 = ___**

- Write the last 2 digits:
**22** - Add the first & last digits: 4 + 2 =
**6**; write this in front. - Write the first 2 digits in front:
**42**. - The answer is
**42622**.

**Example 2: 726 x 101 = ___**

- Write the last 2 digits:
**26** - Add the first & last digits: 7 + 6 =
**13**; write the**3**in front and regroup the**1**. - Write the first 2 digits (plus the regrouped 1) in front:
**73**. - The answer is
**73326**.

**Example 3: 987 x 101 = ___**

- Write
**87**. - 9 + 7 =
**16**; write the**6**in front and regroup the**1**. - Write the 98 (+ 1) in front:
**99**. - The answer is
**99687**.

**Example 4: 314 x 202 = ___**

- Using
**Double/Half**, change this to**628 x 101**. - Write
**28**. - 6 + 2 =
**14**; write the**4**in front and regroup the**1**. - Write the 62 (+ 1) in front:
**63**. - The answer is
**63428**.

**Example 5: 10.1 x 1.72 = ___**

- Don't be deceived by the decimals. Write
**72**. - 1 + 2 =
**3**; write this in front. - Write the
**17**in front. - There are 3 decimal places; the answer is
**17.372**.

**Here's a free worksheet to help you practice Mult101var:**

mult101var.pdf |

**Up Next for Middle School: ConvSpeed**