**High School Number Sense Lesson 19: Multiplying by a Number between 12 and 19 (Inclusive)**

Some people call this the "Teens Trick." I have 3 teenagers, so I know that they can sometimes seem very difficult to handle. But once you get to know them and learn what makes them tick, they can be very helpful and straightforward.

*This concept is no different.*It appeared

**10 times**this year, as early as question 3 and as late as question 39, but on average at

**question # 13**(how appropriate!).

**Number Dojo Level: 170**

This skill works very similarly to Mult11 (if you haven't learned it yet, it may be helpful to start there). You will work from the right to the left. But instead of simply adding neighbors,

**multiply**(by the units digit of your "teen number")

**and add to the right**. I will illustrate the steps with each example.

**Example 1: 13 x 142**

- Look at the units digit of your "teen number" (13), which is 3. We will
**triple and add to the right**. Start with the units digit of your other number. 3 x 2 =**6**; there is nothing to the right of 2, so write**6**down. - 3 x 4 =
**12**, plus the**2**to the right of the 4, equals**14**. Write**4**in front of the 6, and regroup the 1. - 3 x 1 = 3, plus the 4 to the right of the 1, plus the regrouped 1, equals
**8**; write this in front. - 3 x (the implied
**0**in front of the 142) = 0, plus the**1**, equals**1**; write this in front. The answer is**1846**.

**Example 2: 321 x 14**

- Look at the units digit of your "teen number" (14), which is 4. We will
**quadruple and add to the right**. Starting with the units digit of the other number (1)... 4 x 1 =**4**; write this down (since there is nothing to the right to add). - 4 x 2 =
**8**, plus the**1**to the right of the 2, equals**9**. Write this down in front. - 4 x 3 =
**12**, plus the**2**to the right of the 3, equals**14**. Write the**4**and regroup the 1. - 4 x (the implied
**0**in front of the 321) = 0, plus the**3**, plus the regrouped**1**, equals**4**. Write this in front. The answer is**4494**.

**Example 3: 12 x 4213**

- Look at the units digit of your "teen number" (12), which is 2. We will
**double and add to the right**. 2 x 3 =**6**; write this down. - 2 x 1 =
**2**, plus the**3**to the right, equals**5**. Write this down in front. - 2 x 2 =
**4**, plus the**1**to the right, equals**5**. Write this down in front. - 2 x 4 =
**8**, plus the**2**to the right, equals**10**. Write the**0**in front and regroup the 1. - 2 x 0 = 0, plus the
**4**, plus the regrouped**1**, equals**5**. Write this in front. The answer is**50556**.

**Example 4: 4321 x 17**

- Look at the "teens" units digit (7). We will
**multiply by 7 and add to the right**. 7 x 1 =**7**; write this down. - 7 x 2 =
**14**, plus the**1**to the right, equals**15**. Write the**5**in front and regroup the 1. - 7 x 3 =
**21**, plus the**2**to the right, plus the regrouped**1**, equals**24**. Write the**4**in front and regroup the 2. - 7 x 4 =
**28**, plus the**3**to the right, plus the regrouped**2**, equals**33**. Write the**3**in front and regroup the 3. - 7 x 0 = 0, plus the
**4**, plus the regrouped**3**, equals**7**. Write this in front. The answer is**73457**.

**Please note:**It took me about 6 or 7 exposures to this concept for it to click with me. The good news is that most of the time, the numbers the test-writers give you are pretty easy to work with (like 331, 214, 411, etc). Rarely do you get something like

**17 x 879**(where the multiplication of each pair of digits takes a little more thinking). Just like with any other concept, it is best to practice using the

**free worksheet**below.

**Here's a free worksheet to help you practice Mult12-19:**

mult12-19.pdf |

**Up Next for High School: EstDivWhole**