Let's carefully analyze and break down the expression [tex]\(-5\left(2 \frac{1}{16}\right)\)[/tex].
First, convert the mixed number [tex]\(2 \frac{1}{16}\)[/tex] into an improper fraction:
[tex]\[ 2 \frac{1}{16} = 2 + \frac{1}{16} \][/tex]
Thus, the expression becomes:
[tex]\[ -5\left(2 + \frac{1}{16}\right) \][/tex]
Next, we use the distributive property of multiplication over addition:
[tex]\[ -5 \left(2 + \frac{1}{16}\right) = -5(2) + -5\left(\frac{1}{16}\right) \][/tex]
Let's identify each term after the distribution:
1. The first term is:
[tex]\[ -5(2) = -10 \][/tex]
2. The second term is:
[tex]\[ -5\left(\frac{1}{16}\right) = -\frac{5}{16} \][/tex]
Since [tex]\(-\frac{5}{16}\)[/tex] is approximately [tex]\(-0.3125\)[/tex], the values simplify to:
[tex]\[ -5(2) + -5\left(\frac{1}{16}\right) = -10 + -0.3125 \approx -10.3125 \][/tex]
So, the expression that correctly finds [tex]\(-5\left(2 \frac{1}{16}\right)\)[/tex] is:
[tex]\[ -5(2) + (-5)\left(\frac{1}{16}\right) \][/tex]
Thus, the correct choice is:
[tex]\[ -5(2) + (-5)\left(\frac{1}{16}\right) \quad \boxed{} \][/tex]
Therefore, the expression [tex]\(-5\left(2 \frac{1}{16}\right)\)[/tex] can be represented by:
[tex]\[ -5(2) + (-5)\left(\frac{1}{16}\right) \quad \boxed{} \][/tex]
