**High School Number Sense Lesson 31: Multiplying Two Numbers Ending in 5**

Last month we learned how to square any number ending in 5 (

**SquareEnd5**). Now let's learn how to multiply two different numbers ending in 5. This concept showed up

**9 times**on high school tests last year--between questions 5 & 31, with the median at

**question # 19**.

**Number Dojo Level: 95**

Before tackling this concept, it is important to mention that there may be several ways to solve these problems. Here are some opportunities to use a different method than the main one we'll focus on today:

- When one of the factors is
**15**: use Mult15 (which we haven't covered yet) - When one of the factors is
**25**: use**Mult25** - When one of the factors is
**75**: use Mult75 (which we haven't covered yet) - When the factors are
**10 apart**(which we'll cover right now)

**When the Factors are 10 Apart:**

- Add 1 to the larger number's tens digit.
- Multiply this by the other number's tens digit, and write the product down.
- Write a 75 at the end.

**Example 1: 45 x 55**

- Add 1 to the larger number's tens digit. 5 + 1 =
**6**. - Multiply this by the other number's tens digit. 6 x 4 =
**24**; write this down. - Write a
**75**at the end. The answer is**2475**.

**Example 2: 95 x 85**

- Add 1 to the larger number's tens digit. 9 + 1 =
**10**. - Multiply this by the other number's tens digit. 10 x 8 =
**80**; write this down. - Write a
**75**at the end. The answer is**8075**.

**Example 3: 105 x 115**

- Add 1 to the larger number's tens digit (in this case, use everything in front of the 5). 11 + 1 =
**12**. - Multiply this by the other number's tens digit (in this case, use everything in front of the 5). 12 x 10 =
**120**; write this down. - Write a
**75**at the end. The answer is**12075**.

**Any Other Time:**

- If both tens digits are even, or if both are odd, the product will end in
**25**. - If one tens digit is even and the other is odd, the product will end in
**75**.

**How to Solve:**

- Multiply the tens digits and remember this product.
- Take the average of the tens digits (round down to an integer if necessary).
- Add this average to the product found in Step 1. Write this sum down.
- Finish the answer with a 25 or 75 as determined above.

**Example 4: 45 x 85**

- Multiply the tens digits: 4 x 8 =
**32**; remember this product. - Take the average of the tens digits. (4 + 8)/2 = 12/2 =
**6**. - Add this average to the product from Step 1. 32 + 6 =
**38**; write this down. - Both tens digits were even, so write down a
**25**at the end. The answer is**3825**.

**Example 5: 55 x 95**

- Multiply the tens digits: 5 x 9 =
**45**; remember this. - Average the tens digits: (5 + 9)/2 = 14/2 =
**7**. - Add this average to the product from Step 1. 45 + 7 =
**52**; write this down. - Both tens digits were odd, so write a
**25**at the end. The answer is**5225**.

**Example 6: 35 x 65**

- Multiply the tens digits: 3 x 6 =
**18**; remember this. - Average the tens digits: (3 + 6)/2 = 9/2 = 4.5. Round down to
**4**. - Add this to the product from Step 1. 18 + 4 =
**22**; write this down. - One tens digit was even and one was odd, so write a
**75**at the end. The answer is**2275**.

**Example 7: 105 x 55**

- Multiply the tens digits: 10 x 5 =
**50**; remember this. - Average the tens digits: (10 + 5)/2 = 15/2 = 7.5. Round this down to
**7**. - Add this to the product from Step 1. 50 + 7 =
**57**; write this down. - One tens digit was even and the other was odd, so write a
**75**at the end. The answer is**5775**.

**Here's a free worksheet to help you practice MultEnd5:**

multend5.pdf |

**Up Next for High School: FindLCM**