Verify the property \( a \times (b + c) = a \times b + a \times c \) by taking \( a = -\frac{5}{2} \), \( b = \frac{11}{8} \).

To verify the property \( a \times (b + c) = a \times b + a \times c \), let's first calculate the left-hand side (LHS) and the right-hand side (RHS) of the equation separately using the given values for \( a \) and \( b \), and then choose a value for \( c \).

Given: \( a = -\frac{5}{2} \) \( b = \frac{11}{8} \)

Let's choose \( c \) to be a generic value since it wasn't provided in the question. To make the calculation simpler, we can take \( c = \frac{1}{8} \). Now let's calculate both sides of the equation.

LHS: \( a \times (b + c) \) We need to add \( b \) and \( c \) first and then multiply by \( a \): \( b + c = \frac{11}{8} + \frac{1}{8} = \frac{11 + 1}{8} = \frac{12}{8} = \frac{3}{2} \) Now multiply by \( a \): \( a \times (b + c) = -\frac{5}{2} \times \frac{3}{2} = -\frac{5 \times 3}{2 \times 2} = -\frac{15}{4} \)

RHS: \( a \times b + a \times c \) We need to multiply \( a \) by \( b \) and by \( c \) separately, and then add those results: \( a \times b = -\frac{5}{2} \times \frac{11}{8} = -\frac{5 \times 11}{2 \times 8} = -\frac{55}{16} \) \( a \times c = -\frac{5}{2} \times \frac{1}{8} = -\frac{5 \times 1}{2 \times 8} = -\frac{5}{16} \) Adding \( a \times b \) and \( a \times c \): \( RHS = -\frac{55}{16} + -\frac{5}{16} = -\frac{55 + 5}{16} = -\frac{60}{16} = -\frac{15}{4} \)

Comparing both sides: LHS = -\frac{15}{4} RHS = -\frac{15}{4}

Since both LHS and RHS are equal, we have verified the property \( a \times (b + c) = a \times b + a \times c \) with the given values of \( a \) and \( b \), and our choice of \( c \).