Question 6

We will calculate both sides of the equation separately.

Step 1 — Calculate the Left Side

Let's find the value of the left side. First, we add the fractions inside the bracket. We find a common denominator for 2 and 4.

$\frac{1}{2} + \frac{3}{4} = \frac{1 \times 2}{2 \times 2} + \frac{3}{4}$

$= \frac{2}{4} + \frac{3}{4}$

$= \frac{2+3}{4}$

$= \frac{5}{4}$

Now, we multiply this sum by $\frac{8}{3}$.

$\left(\frac{5}{4}\right) \times \frac{8}{3} = \frac{5 \times 8}{4 \times 3}$

$= \frac{40}{12}$

We simplify the fraction by dividing by 4.

$\boxed{\frac{10}{3}}$

Step 2 — Calculate the Right Side

Let's find the value of the right side. First, we multiply $\frac{1}{2}$ by $\frac{8}{3}$.

$\frac{1}{2} \times \frac{8}{3} = \frac{1 \times 8}{2 \times 3}$

$= \frac{8}{6}$

We simplify this fraction by dividing by 2.

$= \frac{4}{3}$

Next, we multiply $\frac{3}{4}$ by $\frac{8}{3}$.

$\frac{3}{4} \times \frac{8}{3} = \frac{3 \times 8}{4 \times 3}$

$= \frac{24}{12}$

We simplify this fraction by dividing by 12.

$= 2$

Finally, we add these two results.

$\frac{4}{3} + 2 = \frac{4}{3} + \frac{2 \times 3}{3}$

$= \frac{4}{3} + \frac{6}{3}$

$= \frac{4+6}{3}$

$\boxed{\frac{10}{3}}$

Answer

(i) The left side of the equation is $\frac{10}{3}$. (ii) The right side of the equation is $\frac{10}{3}$. (iii) Since both sides are equal to $\frac{10}{3}$, the given statement is shown to be true.