**Elementary School Number Sense Lesson 23: Estimating with Multiplication using the Distributive Property**

These problems require the same skills used with

**MultDistrib2**, but they also require estimation. They show up on every level of number sense competitions (elementary, middle, and high school). They have appeared

**4 times**so far in elementary school this year, with placement at

**question # 70**or 80.

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To solve these problems, you may need to round or manipulate some of the numbers until there is a common factor. Then you may need to round again to simplify the multiplication.

**Example 1: * 82 x 22 – 41 x 21 = ___**

- Use
**Double/Half**in with**82 x 22**to get**41 x 44**, which makes the problem**41 x 44 – 41 x 21**. - Factor out 41 to get
**41 x (44 – 21)**, which is**41 x 23**. - Round 41 down to 40 and multiply by 23. Your answer is
**920**. - The exact answer is
**943**, and the acceptable (+/- 5%) range is**from 896 to 990**.

**Example 2: * 82 x 23 – 51 x 24 = ___**

- Change the 24 to a 23, so the problem becomes
**82 x 23 – 51 x 23**. - Factor out 23 to get
**(82 – 51) x 23**, which is**31 x 23**. - Round 31 down to 30, and multiply by 23. Your answer is
**690**. - The exact answer is
**662**, and the acceptable (+/- 5%) range is**from 629 to 695**.

**Example 3: * 32 x 49 + 38 x 51 = ___**

- Round both 49 and 51 to
**50**, so the problem becomes**32 x 50 + 38 x 50**. - Factor out 50 to get
**(32 + 38) x 50**, which is**70 x 50**. - Your answer is
**3500**. - The exact answer is
**3506**, and the acceptable (+/- 5%) range is**from 3331 to 3681**.

**Example 4: * 73 x 44 + 77 x 65 = ___**

- Round both 73 and 77 to
**75**, so the problem becomes**75 x 44 + 75 x 65**. - Factor out 75 to get
**75 x (44 + 65)**, which is**75 x 109**. - Round 109 to 110 and multiply by 75. Your answer is
**8250**. - The exact answer is
**8217**, and the acceptable (+/- 5%) range is**from 7807 to 8627**.

**Example 5: * 72 x 48 + 72 x 351 = ___**

- Factor 72 out to get
**72 x (48 + 351)**, which is**72 x 399**. - Round 399 to 400 and multiply by 72. Your answer is
**28800**. - The exact answer is
**28728**, and the acceptable (+/- 5%) range is**from 27292 to 30164**.

**Here's a free worksheet to help you practice EstMultDistr2:**

estmultdistr2.pdf |

**Up Next for Elementary School: Square2Digit**