Compute. $$ \frac{5}{34} \cdot 22 \frac{2}{3}-2 \frac{1}{9} $$

Question

UpStudy AI · Accepted Answer

To compute the expression:

$$
\frac{5}{34} \cdot 22 \frac{2}{3} - 2 \frac{1}{9}
$$

**Step 1: Convert Mixed Numbers to Improper Fractions**

1. $$22 \frac{2}{3}$$:
   $$
   22 \frac{2}{3} = \frac{22 \times 3 + 2}{3} = \frac{68}{3}
   $$

2. $$2 \frac{1}{9}$$:
   $$
   2 \frac{1}{9} = \frac{2 \times 9 + 1}{9} = \frac{19}{9}
   $$

**Step 2: Multiply $$\frac{5}{34}$$ by $$\frac{68}{3}$$**

$$
\frac{5}{34} \times \frac{68}{3}
$$

Simplify before multiplying:

- $$68 \div 34 = 2$$, so:
  
$$
\frac{5}{34} \times \frac{68}{3} = \frac{5 \times 2}{3} = \frac{10}{3}
$$

**Step 3: Subtract $$\frac{19}{9}$$ from $$\frac{10}{3}$$**

Convert $$\frac{10}{3}$$ to ninths to have a common denominator:

$$
\frac{10}{3} = \frac{30}{9}
$$

Now subtract:

$$
\frac{30}{9} - \frac{19}{9} = \frac{11}{9} = 1 \frac{2}{9}
$$

**Final Answer:**

$$
1 \frac{2}{9}
$$
The final answer is $$1 \frac{2}{9}$$.

Compute.