First, evaluate the inner expression 2 - (1)/(2) = (3)/(2). Then subtract (1)/(4) by finding the common denominator 4: (6)/(4) - (1)/(4) = (5)/(4).

Inside the parentheses, -(1)/(2) - (1)/(4) = -(3)/(4). Then 2 - (3)/(4) = (8)/(4) - (3)/(4) = (5)/(4). Since LHS = RHS = (5)/(4), the associative property (a+b)+c = a+(b+c) is verified.

Verify (a+b)+c the value of a is to the value of B is -1/2 and the value of C is -1/ 4

Answer: $\text{LHS} = \text{RHS} = \frac{5}{4}$ , hence $(a+b)+c = a+(b+c)$ is verified.

Step-by-step solution

Step 1: Evaluate Left-Hand Side (LHS)

We begin by evaluating the expression on the left-hand side, $(a + b) + c$ . Substitute $a = 2$ , $b = -\frac{1}{2}$ , and $c = -\frac{1}{4}$ into the grouping.

Step 2: Simplify the Left-Hand Side

First, evaluate the inner expression $2 - \frac{1}{2} = \frac{3}{2}$ . Then subtract $\frac{1}{4}$ by finding the common denominator $4$ : $\frac{6}{4} - \frac{1}{4} = \frac{5}{4}$ .

Step 3: Evaluate Right-Hand Side (RHS)

Now we evaluate the right-hand side, $a + (b + c)$ , using the associative regrouping. Substitute $a = 2$ , $b = -\frac{1}{2}$ , and $c = -\frac{1}{4}$ .

Step 4: Simplify the Right-Hand Side and Verify

Inside the parentheses, $-\frac{1}{2} - \frac{1}{4} = -\frac{3}{4}$ . Then $2 - \frac{3}{4} = \frac{8}{4} - \frac{3}{4} = \frac{5}{4}$ . Since $\text{LHS} = \text{RHS} = \frac{5}{4}$ , the associative property $(a+b)+c = a+(b+c)$ is verified.

Solve your own maths question free →