Question

$-\frac{1}{2} div left(2\frac{3}{4} + 2\frac{1}{4}
ight)$

Explanation:

Step1: Calculate the sum inside the parentheses

First, add the mixed numbers \(2\frac{3}{4}\) and \(2\frac{1}{4}\). Since the fractions have the same denominator, we can add the whole numbers and the fractions separately. The whole numbers: \(2 + 2 = 4\). The fractions: \(\frac{3}{4}+\frac{1}{4}=\frac{3 + 1}{4}=\frac{4}{4}=1\). Then, add the results: \(4+1 = 5\). So, \(2\frac{3}{4}+2\frac{1}{4}=5\).

Step2: Perform the division operation

Now, we have \(-\frac{1}{2}\div5\). Recall that dividing by a number is the same as multiplying by its reciprocal. So, \(-\frac{1}{2}\div5=-\frac{1}{2}\times\frac{1}{5}\).

Step3: Multiply the fractions

Multiply the numerators and the denominators: \(-\frac{1\times1}{2\times5}=-\frac{1}{10}\).

Answer:

\(-\frac{1}{10}\)