Certainly! Let's break down the given expression step by step.
[tex]\[
\frac{49}{9} \div 7 + \left(3 - \frac{11}{7}\right) \div \left( \frac{14}{44} + \frac{3}{7} \div \frac{1}{12} \right)
\][/tex]
### Step 1: Simplify [tex]\(\frac{49}{9} \div 7\)[/tex]
To divide fractions, we multiply by the reciprocal:
[tex]\[
\frac{49}{9} \div 7 = \frac{49}{9} \times \frac{1}{7} = \frac{49 \times 1}{9 \times 7} = \frac{49}{63} = \frac{7}{9} \approx 0.7777777777777778
\][/tex]
### Step 2: Simplify [tex]\(3 - \frac{11}{7}\)[/tex]
First, get a common denominator:
[tex]\[
\frac{21}{7} - \frac{11}{7} = \frac{21 - 11}{7} = \frac{10}{7} \approx 1.4285714285714286
\][/tex]
### Step 3: Simplify [tex]\(\frac{14}{44} + \frac{3}{7} \div \frac{1}{12}\)[/tex]
First, simplify [tex]\(\frac{3}{7} \div \frac{1}{12}\)[/tex]:
[tex]\[
\frac{3}{7} \div \frac{1}{12} = \frac{3}{7} \times \frac{12}{1} = \frac{3 \times 12}{7 \times 1} = \frac{36}{7} \approx 5.142857142857143
\][/tex]
Next, simplify [tex]\(\frac{14}{44}\)[/tex]:
[tex]\[
\frac{14}{44} = \frac{7}{22} \approx 0.3181818181818182
\][/tex]
Now add [tex]\(\frac{7}{22}\)[/tex] and [tex]\(\frac{36}{7}\)[/tex]:
[tex]\[
0.3181818181818182 + \frac{36}{7} \approx 0.3181818181818182 + 5.142857142857143 \approx 5.461038961038962
\][/tex]
### Step 4: Put it all together
Now, we have:
[tex]\[
\left(3 - \frac{11}{7}\right) \div \left(\frac{14}{44} + \frac{3}{7} \div \frac{1}{12}\right)
\][/tex]
This becomes:
[tex]\[
1.4285714285714286 \div 5.461038961038962 \approx 0.2611126606671038
\][/tex]
Finally, add this to our result from Step 1:
[tex]\[
\frac{49}{9} \div 7 + 0.2611126606671038 \approx 0.7777777777777778 + 0.03933488288932594 \approx 0.8171126606671038
\][/tex]
Thus, the final result is:
[tex]\[
\boxed{0.8171126606671038}
\][/tex]
