Sure, I'll address each part of these questions step by step.
### Question 1
To solve the given expression:
[tex]\[ \frac{6}{4} - \frac{9}{12} \cdot \cdot 2 \frac{5^4}{39} - \frac{2}{16} \][/tex]
First, we simplify each part separately.
1. Simplify [tex]\(\frac{6}{4}\)[/tex]:
[tex]\[ \frac{6}{4} = \frac{3}{2} \][/tex]
2. Simplify [tex]\(\frac{9}{12}\)[/tex]:
[tex]\[ \frac{9}{12} = \frac{3}{4} \][/tex]
3. Calculate [tex]\(5^4\)[/tex]:
[tex]\[ 5^4 = 625 \][/tex]
4. Simplify [tex]\(\frac{5^4}{39}\)[/tex]:
[tex]\[ \frac{625}{39} = \text{Irreducible fraction} \][/tex]
5. Simplify [tex]\(\frac{2}{16}\)[/tex]:
[tex]\[ \frac{2}{16} = \frac{1}{8} \][/tex]
Combining all parts together:
[tex]\[ \frac{3}{2} - \frac{3}{4} \cdot \cdot 2 \frac{625}{39} - \frac{1}{8} \][/tex]
Now let’s simplify the complete expression:
[tex]\[ (\frac{3}{2} - \frac{3}{4}) = (1.5 - 0.75) = 0.75\][/tex]
[tex]\[ 0.75 0.75 \frac{625}{39} - \frac{1}{8}\][/tex]
[tex]\[ \frac{16.40625}{39} -\frac{1}{8}\][/tex]
[Need more simplification, answer pending]
### Question 2
Let's interpret this as it’s written in non-standard form
### Question 3
We have [tex]\(\frac{45}{4}\)[/tex]:
This fraction is already in its simplest form, so the answer is:
[tex]\[ \frac{45}{4} \][/tex]
### Question 4
To solve the given fractional expressions:
[tex]\[ \frac{5}{4} - \frac{3}{6} \][/tex]
[tex]\[ 5 \frac{3}{\frac{1}{7}} + \frac{5}{3}\][/tex]
1. Simplify [tex]\(\frac{5}{4} - \frac{3}{6}\)[/tex]:
[tex]\[ \frac{3}{6} = \frac{1}{2} \][/tex]
[tex]\[ \frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \][/tex]
2. Simplify [tex]\(5 \frac{3}{\frac{1}{7}} + \frac{5}{3}\)[/tex]:
[tex]\[ \frac{3}{\frac{1}{7}} = 3 \times 7 = 21 \][/tex]
[tex]\[ 5 \times 21 = 105 \][/tex]
[tex]\[ 105 + \frac{5}{3} = \][/tex]
Combining:
Answer: [tex]$\frac{5}{4} - \frac{3}{6} = \frac{3}{4}, 210$[/tex]
