Which property is shown by –5 • (6 + 7) = –5 • 6 + (–5) • 7?
Look up the property of the distributive property
commutative
The property shown in the equation –5 • (6 + 7) = –5 • 6 + (–5) • 7 is the Distributive Property.
The property that is shown by –5 • (6 + 7) = –5 • 6 + (–5) • 7 is called the distributive property.
To understand this property, let's break down the equation step by step:
Step 1: –5 • (6 + 7)
In this step, we have the expression –5 multiplied by the sum of 6 and 7. To simplify this, we first need to evaluate the sum inside the parentheses, which gives us 13. Then, we multiply –5 by 13, resulting in -65.
Step 2: –5 • 6 + (–5) • 7
In this step, we have –5 multiplied by 6, which gives us -30. Then we have –5 multiplied by 7, which gives us -35. Finally, we add -30 and -35 together, resulting in -65.
Since the value of the expression is the same on both sides of the equation (-65), we can conclude that the distributive property is being used here. The distributive property states that when we multiply a number by the sum of two or more numbers, we can distribute the multiplication to each term individually and then perform the addition. In other words:
a • (b + c) = (a • b) + (a • c)
In our example, a is -5, b is 6, and c is 7. Therefore, –5 • (6 + 7) = –5 • 6 + (–5) • 7 demonstrates the distributive property.