  ### Home > CC2MN > Chapter 2 > Lesson 2.2.4 > Problem2-80

2-80.

Use the Distributive Property to rewrite each of the following products as sums, and then calculate the value, as shown in the example below.

Example: $4(307)=4(300)+4(7)=$$1200+28=1228$

1. $9(410)$

As seen in the example above, it helps to separate the larger number into parts. It would be best to separate it into parts by place value (hundreds, tens, ones). This way, you will be able to multiply each part of the sum more easily.

The product of this expression is $3690$. Remember to show how you rewrote the product as a sum!

1. $6(592)$

Here, try thinking of $592$ as $600+(−8)$. This way you can use the same method as in part (a).

When separating the number into parts, remember that 8 is now negative. Also, when multiplying, negative numbers are like steps backwards, so the product will also be negative.

This product can be written as a sum this way: $6(600)+6(−8)$ or $6(600+(−8))$. You can also simplify it by multiplying each part of the sum: $3600+(−48)=3552$.