17. $$ \frac{3}{4}\left(\frac{4}{3}+\frac{8}{9}\right)= $$

Question

UpStudy AI · Accepted Answer

To solve the expression:

$$
\frac{3}{4} \left( \frac{4}{3} + \frac{8}{9} \right)
$$

**Step 1: Simplify inside the parentheses**

First, add $$\frac{4}{3}$$ and $$\frac{8}{9}$$:

$$
\frac{4}{3} + \frac{8}{9}
$$

To add these fractions, find a common denominator. The least common denominator (LCD) of 3 and 9 is 9.

$$
\frac{4}{3} = \frac{12}{9} \quad (\text{multiply numerator and denominator by 3})
$$

Now, add the fractions:

$$
\frac{12}{9} + \frac{8}{9} = \frac{20}{9}
$$

**Step 2: Multiply by $$\frac{3}{4}$$**

Now, multiply $$\frac{3}{4}$$ by $$\frac{20}{9}$$:

$$
\frac{3}{4} \times \frac{20}{9} = \frac{60}{36}
$$

**Step 3: Simplify the fraction**

Simplify $$\frac{60}{36}$$ by dividing both the numerator and the denominator by their greatest common divisor, which is 12:

$$
\frac{60 \div 12}{36 \div 12} = \frac{5}{3}
$$

So, the simplified result is:

$$
\boxed{\dfrac{5}{3}}
$$
The result is $$\frac{5}{3}$$.

17. \( \frac{3}{4}\left(\frac{4}{3}+\frac{8}{9}\right)= \)