Distributive Property of Real Numbers

Mary has a vegetable garden that is 6 meters wide and 9 meters long. To grow more vegetables, she decides to add an extra section that is x meters long.

Before planting, Mary wants to find the area of the extended garden. With a length of 9 plus x meters, the area is 6 times the quantity 9 plus x. The distributive property of real numbers helps rewrite this expression.

It states that multiplying a number by a sum is the same as multiplying the number by each term and then adding the results.

Using this property, 6 times the quantity 9 plus x can be rewritten as 6 times 9 plus 6 times x. Simplifying the expression gives 54 plus 6x.

Later, Mary decides to remove a y-meter-long section along the extended garden’s length to make room for a walkway. So, the area of the remaining garden is 6 times the quantity 9 plus x minus y.

The distributive property also works with more than two terms. Multiplying 6 by each term gives 54 plus 6x minus 6y.

Whether adding or subtracting, the distributive property simplifies expressions into easier-to-manage parts.