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[tex]
\begin{array}{l}
5 \frac{3}{7} = 6 \frac{2}{7} + 1 \frac{3}{7} - 2 \frac{2}{7} \\
1 \frac{9}{12} = \frac{45}{12} - \frac{27}{12} + \frac{3}{12}
\end{array}
[/tex]

Answer :

Let's solve the given equations step-by-step.

### First Equation:
[tex]\[ 5 \frac{3}{7}=6 \frac{2}{7}+1 \frac{3}{7}-2 \frac{2}{7} \][/tex]

1. Convert the mixed numbers to improper fractions or decimal form for easier calculation.
- [tex]\(5 \frac{3}{7} = 5 + \frac{3}{7} \)[/tex]
- [tex]\(6 \frac{2}{7} = 6 + \frac{2}{7} \)[/tex]
- [tex]\(1 \frac{3}{7} = 1 + \frac{3}{7} \)[/tex]
- [tex]\(-2 \frac{2}{7} = -2 - \frac{2}{7} \)[/tex]

2. Calculate the left-hand side of the equation:
- [tex]\(5 + \frac{3}{7} \approx 5.428571428571429\)[/tex]

3. Calculate the right-hand side:
- [tex]\(6 + \frac{2}{7} = 6 + 0.285714 \approx 6.285714\)[/tex]
- [tex]\(1 + \frac{3}{7} = 1 + 0.428571 \approx 1.428571\)[/tex]
- [tex]\(-2 - \frac{2}{7} = -2 - 0.285714 \approx -2.285714\)[/tex]

4. Sum the right-hand side values:
- [tex]\(6.285714 + 1.428571 - 2.285714 \approx 5.428571\)[/tex]

So, [tex]\(5 \frac{3}{7} = 6 \frac{2}{7} + 1 \frac{3}{7} - 2 \frac{2}{7}\)[/tex]
[tex]\[ 5.428571428571429 = 5.428571428571429 \][/tex]

### Second Equation:
[tex]\[ 1 \frac{9}{12}=\frac{45}{12}-\frac{27}{12}+\frac{3}{12} \][/tex]

1. Convert the fractions to a common form for easier calculation:
- [tex]\(1 \frac{9}{12} = 1 + \frac{9}{12} \)[/tex]
- [tex]\(1 + \frac{9}{12} = 1 + 0.75 = 1.75\)[/tex]

2. Calculate the right-hand side:
- [tex]\(\frac{45}{12} \approx 3.75\)[/tex]
- [tex]\(\frac{27}{12} \approx 2.25\)[/tex]
- [tex]\(\frac{3}{12} \approx 0.25\)[/tex]

3. Sum the right-hand side values:
- [tex]\( 3.75 - 2.25 + 0.25 = 1.75 \)[/tex]

So, [tex]\(1 \frac{9}{12} = \frac{45}{12} - \frac{27}{12} + \frac{3}{12}\)[/tex]
[tex]\[ 1.75 = 1.75 \][/tex]

Both equations are correct as they hold true in their respective values.

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