**Middle School Number Sense Lesson 12: Divide by Doubling First**

Why multiply when asked to divide? Because sometimes it's just better, that's why! In certain situations (such as when dividing by a fraction or decimal), it is easier to work with the numbers if you double them first. I counted 9 times this year that such a situation showed up on middle school tests--as early as question # 2 and as late as question # 21, but on average at

**question # 12**.

**Number Dojo Level: 62**

This skill works best when the

**divisor ends in 5**(or .5 or 1/2). Imagine you are asked to divide 65 by 5. It may come quickly to you that the answer is 13, but it may not. What if you doubled both 65 and 5 to get

**130 ÷ 10**? You can easily see that the answer is

**13**. Doubling first may or may not save you time on this example, but let's look at a few examples where it will definitely save time.

**Example 1: 28 ÷ 3.5**

- Notice that the divisor ends in 5. Double both the dividend and the divisor. 28 x 2 =
**56**, and 3.5 x 2 =**7**. - Divide the new numbers: 56 ÷ 7 =
**8**.

**Example 2: 18 ÷ 1 1/2**

- Notice that the divisor ends in 1/2. Double both the dividend and the divisor. 18 x 2 =
**36**, and 1 1/2 x 2 =**3**. - Divide the new numbers: 36 ÷ 3 =
**12**.

**Example 3: 19 ÷ 5 = ___ decimal**

- Notice that the divisor ends in (is actually) 5. Double both the dividend and the divisor. 19 x 2 =
**38**and 5 x 2 =**10**. - Divide the new numbers. 38 ÷ 10 =
**3.8**

**Example 4: 25 ÷ 1.25**

- Notice that the divisor ends in 5. Double both the dividend and the divisor. 25 x 2 =
**50**and 1.25 x 2 =**2.5**. - Notice that the divisor still ends in 5. Double both again. 50 x 2 =
**100**and 2.5 x 2 =**5**. - Divide the new numbers. 100 ÷ 5 =
**20.**

**Here's a free worksheet to help you practice DivDouble1st:**

divdouble1st.pdf |

**Up Next for Middle School: ConvDistEng**