To understand the property Terry is using, let's break down the expression step-by-step.
We start with the given expression:
[tex]\[ 8\left(-5 \frac{1}{4}\right) \][/tex]
Terry is simplifying this expression and writes it as:
[tex]\[ 8\left(-5 \frac{1}{4}\right) = 8(-5) + 8\left(-\frac{1}{4}\right) \][/tex]
Terry is breaking down the mixed number [tex]\(-5 \frac{1}{4}\)[/tex] into two separate terms: [tex]\(-5\)[/tex] and [tex]\(-\frac{1}{4}\)[/tex].
The property that allows Terry to separate the multiplication over the addition inside the expression (since subtraction can be viewed as the addition of a negative number) is known as the distributive property. According to the distributive property, you can distribute the multiplication over addition or subtraction inside the parentheses.
To recap, Terry uses the distributive property to simplify:
[tex]\[ 8\left(-5 \frac{1}{4}\right) = 8(-5) + 8\left(-\frac{1}{4}\right) \][/tex]
Thus, the property Terry is using is the distributive property.
