Simplifying Proper Fractions (J) Simplify each fraction to its lowest terms $$ \frac{30: 3}{48}: \frac{10: 2}{16: 2}=\left(\frac{5}{8} \quad \frac{27}{99}: \frac{3}{a}=\frac{3}{11} \quad\right. $$

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Let's simplify each fraction step by step.

1. **Simplifying the first fraction:**
   $$
   \frac{30:3}{48}
   $$
   First, we simplify $$30:3$$:
   $$
   30:3 = 10
   $$
   So, the fraction becomes:
   $$
   \frac{10}{48}
   $$
   Now, we simplify $$\frac{10}{48}$$:
   - The greatest common divisor (GCD) of 10 and 48 is 2.
   $$
   \frac{10 \div 2}{48 \div 2} = \frac{5}{24}
   $$

2. **Simplifying the second fraction:**
   $$
   \frac{10:2}{16:2}
   $$
   First, we simplify $$10:2$$ and $$16:2$$:
   $$
   10:2 = 5 \quad \text{and} \quad 16:2 = 8
   $$
   So, the fraction becomes:
   $$
   \frac{5}{8}
   $$

3. **Now, we have:**
   $$
   \frac{5}{24} : \frac{5}{8}
   $$
   Dividing fractions is the same as multiplying by the reciprocal:
   $$
   \frac{5}{24} \times \frac{8}{5}
   $$
   The $$5$$ in the numerator and denominator cancels out:
   $$
   \frac{8}{24}
   $$
   Now, we simplify $$\frac{8}{24}$$:
   - The GCD of 8 and 24 is 8.
   $$
   \frac{8 \div 8}{24 \div 8} = \frac{1}{3}
   $$

4. **Next, we simplify the third fraction:**
   $$
   \frac{27}{99}
   $$
   The GCD of 27 and 99 is 9.
   $$
   \frac{27 \div 9}{99 \div 9} = \frac{3}{11}
   $$

5. **Now, we have:**
   $$
   \frac{3}{a} = \frac{3}{11}
   $$
   To find $$a$$, we can set the fractions equal to each other:
   $$
   3 \cdot 11 = 3 \cdot a
   $$
   This simplifies to:
   $$
   33 = 3a
   $$
   Dividing both sides by 3 gives:
   $$
   a = 11
   $$

### Summary of Results:
- The simplified form of $$\frac{30:3}{48} : \frac{10:2}{16:2}$$ is $$\frac{1}{3}$$.
- The value of $$a$$ is $$11$$.
The simplified results are: - $$\frac{30:3}{48} : \frac{10:2}{16:2} = \frac{1}{3}$$ - $$a = 11$$

Simplifying Proper Fractions (J)
Simplify each fraction to its lowest terms

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