**Middle School Number Sense Lesson 21: Double One Factor and take Half the Other when Multiplying**

This concept was one of the first number sense skills I ever learned (right up there with Mult11). It comes in handy in a lot of cases, but especially when multiplying with decimals or fractions. On this year's tests, it appeared (at least)

**7 times**in middle school, usually around

**question # 21**.

**Number Dojo Level: 43**

The idea is simple--when multiplying two or more numbers, you can take a factor out of one and multiply it by the other to make the multiplication simpler. For example, 45 x 16 is not a quick-and-easy multiplication problem. But if you factor out a 2 from the 16 and multiply it by the 45, you are left with 90 x 8. Most people can solve this new problem in about a second: 720. Double/Half is really just a multiplication skill.

**Use Double/Half when one of the factors is even, and the other factor:**

- Is a whole number that
**ends in 5**, - Is a mixed number or fraction with a
**denominator of 2 or 4**, or - Is a decimal that
**ends in .5 or .25**, etc.

**How to Solve:**

- Take half the even number.
- Double the other factor.
- Multiply these new (easier) factors together, or repeat steps 1 & 2 first.

**Example 1: 15 x 18**

- Take half the even number (18) to get
**9**. - Double the other number (15) to get
**30**. - 9 x 30 =
**270**.

**Example 2: 24 x 3 1/2**

- 24 ÷ 2 =
**12** - 2 x (3 1/2) =
**7** - 12 x 7 =
**84**.

**Example 3: 4.5 x 14**

- 14 ÷ 2 =
**7** - 4.5 x 2 =
**9** - 7 x 9 =
**63**.

**Example 4: 5 x 486**

- 48 ÷ 2 =
**243** - 5 x 2 =
**10** - 243 x 10 =
**2430**

**Example 5: 8 x 7.25**

- 8 ÷ 2 =
**4** - 7.25 x 2 =
**14.5** - Repeat steps 1 & 2. 4 ÷ 2 =
**2**, and 14.5 x 2 =**29**. 2 x 29 =**58**.

**Example 6: 16 x (11 1/4)**

- 16 ÷ 2 =
**8** - (11 1/4) x 2 =
**22 1/2** - Repeat steps 1 & 2. 8 ÷ 2 =
**4**, and 22 1/2 x 2 =**45**. - Repeat steps 1 & 2. 4 ÷ 2 =
**2**, and 45 x 2 =**90**. 2 x 90 =**180**.

**Here's a free worksheet to help you practice Double/Half:**

doublehalf.pdf |

**And a video.**

Up Next for Middle School: DiffSquares1

Up Next for Middle School: DiffSquares1