Complete the paftern. a. $$ \frac{5}{6} \cdot 2=\frac{10}{12} \cdot 2=\frac{20}{24} \cdot 2=-=\square=\square $$ b. $$ \frac{3}{4}=\frac{9}{12}=\frac{27}{36}=-=\square=\square $$ c. $$ \frac{9}{11}=\frac{18}{22}=\frac{36}{44}=\square=\square $$ d. $$ \frac{1}{7}=\frac{5}{35}=\frac{25}{175}=\square=\square=\square $$

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To complete the patterns, we need to identify the relationship between the fractions in each sequence. Each fraction seems to be multiplied by a certain factor to generate the next fraction in the sequence. Let's analyze each part step by step.

### a. 
The pattern starts with $$ \frac{5}{6} $$ and each subsequent fraction is obtained by multiplying both the numerator and denominator by 2.

1. $$ \frac{5}{6} \cdot 2 = \frac{10}{12} $$
2. $$ \frac{10}{12} \cdot 2 = \frac{20}{24} $$
3. Continuing this pattern:
   - $$ \frac{20}{24} \cdot 2 = \frac{40}{48} $$
   - $$ \frac{40}{48} \cdot 2 = \frac{80}{96} $$

So, the completed sequence is:
$$
\frac{5}{6} \cdot 2 = \frac{10}{12} \cdot 2 = \frac{20}{24} \cdot 2 = \frac{40}{48} = \frac{80}{96}
$$

### b. 
The pattern starts with $$ \frac{3}{4} $$ and each subsequent fraction is obtained by multiplying both the numerator and denominator by 3.

1. $$ \frac{3}{4} \cdot 3 = \frac{9}{12} $$
2. $$ \frac{9}{12} \cdot 3 = \frac{27}{36} $$
3. Continuing this pattern:
   - $$ \frac{27}{36} \cdot 3 = \frac{81}{108} $$
   - $$ \frac{81}{108} \cdot 3 = \frac{243}{324} $$

So, the completed sequence is:
$$
\frac{3}{4} = \frac{9}{12} = \frac{27}{36} = \frac{81}{108} = \frac{243}{324}
$$

### c. 
The pattern starts with $$ \frac{9}{11} $$ and each subsequent fraction is obtained by multiplying both the numerator and denominator by 2.

1. $$ \frac{9}{11} \cdot 2 = \frac{18}{22} $$
2. $$ \frac{18}{22} \cdot 2 = \frac{36}{44} $$
3. Continuing this pattern:
   - $$ \frac{36}{44} \cdot 2 = \frac{72}{88} $$
   - $$ \frac{72}{88} \cdot 2 = \frac{144}{176} $$

So, the completed sequence is:
$$
\frac{9}{11} = \frac{18}{22} = \frac{36}{44} = \frac{72}{88} = \frac{144}{176}
$$

### d. 
The pattern starts with $$ \frac{1}{7} $$ and each subsequent fraction is obtained by multiplying both the numerator and denominator by 5.

1. $$ \frac{1}{7} \cdot 5 = \frac{5}{35} $$
2. $$ \frac{5}{35} \cdot 5 = \frac{25}{175} $$
3. Continuing this pattern:
   - $$ \frac{25}{175} \cdot 5 = \frac{125}{875} $$
   - $$ \frac{125}{875} \cdot 5 = \frac{625}{4375} $$

So, the completed sequence is:
$$
\frac{1}{7} = \frac{5}{35} = \frac{25}{175} = \frac{125}{875} = \frac{625}{4375}
$$

### Final Answers:
a. $$ \frac{40}{48} = \frac{80}{96} $$

b. $$ \frac{81}{108} = \frac{243}{324} $$

c. $$ \frac{72}{88} = \frac{144}{176} $$

d. $$ \frac{125}{875} = \frac{625}{4375} $$
a. $$ \frac{40}{48} = \frac{80}{96} $$ b. $$ \frac{81}{108} = \frac{243}{324} $$ c. $$ \frac{72}{88} = \frac{144}{176} $$ d. $$ \frac{125}{875} = \frac{625}{4375} $$

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