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The given mathematical expression is a bit unclear and appears to be a mix of several unrelated fractions and operations. Here is a potential reformatting to clarify the expressions, separating the different operations for better readability:

Solve the following expressions:

1. [tex]\[ x \cdot \frac{1}{2} \][/tex]

2. [tex]\[ \frac{1}{4} \times 3 \frac{1}{3} = \frac{1}{8} \times \frac{1}{4} = \frac{1}{12} \][/tex]

3. [tex]\[ \frac{1}{2} \times 3 \frac{2}{3} \][/tex]

4. [tex]\[ \frac{3}{3} + 5 \frac{3}{4} \][/tex]

5. [tex]\[ x \cdot 3 \frac{4}{1} \][/tex]

If the intent was different or if specific details or context were missing, please provide additional clarification.

Sagot :

GinnyAnsweridn
Sure! Let's solve each part of the given expression step by step.

### Part 1: [tex]\( x \frac{1}{2} \)[/tex]
This is equivalent to multiplying [tex]\( x \)[/tex] by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ x \frac{1}{2} = x \times \frac{1}{2} = \frac{x}{2} \][/tex]

So, the result for this part is:
[tex]\[ x \times \frac{1}{2} \][/tex]

### Part 2: [tex]\( \frac{1}{4} \times 3\frac{1}{3} \)[/tex]
First, convert the mixed number [tex]\( 3\frac{1}{3} \)[/tex] into an improper fraction.
[tex]\[ 3\frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \][/tex]

Now multiply:
[tex]\[ \frac{1}{4} \times \frac{10}{3} = \frac{1 \times 10}{4 \times 3} = \frac{10}{12} = \frac{5}{6} \][/tex]

Converting this to a decimal:
[tex]\[ \frac{5}{6} \approx 0.8333333333333334 \][/tex]

So, the result for this part is:
[tex]\[ 0.8333333333333334 \][/tex]

### Part 3: [tex]\( \frac{1}{8} \times \frac{1}{4} \)[/tex]
Multiply the fractions directly:
[tex]\[ \frac{1}{8} \times \frac{1}{4} = \frac{1 \times 1}{8 \times 4} = \frac{1}{32} \][/tex]

Converting this to a decimal:
[tex]\[ \frac{1}{32} = 0.03125 \][/tex]

So, the result for this part is:
[tex]\[ 0.03125 \][/tex]

### Part 4: [tex]\( \frac{1}{2} \times 3\frac{2}{3} \)[/tex]
First, convert the mixed number [tex]\( 3\frac{2}{3} \)[/tex] into an improper fraction.
[tex]\[ 3\frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \][/tex]

Now multiply:
[tex]\[ \frac{1}{2} \times \frac{11}{3} = \frac{1 \times 11}{2 \times 3} = \frac{11}{6} \][/tex]

Converting this to a decimal:
[tex]\[ \frac{11}{6} \approx 1.8333333333333333 \][/tex]

So, the result for this part is:
[tex]\[ 1.8333333333333333 \][/tex]

### Part 5: [tex]\( \frac{3}{3} + 5\frac{3}{4} \)[/tex]
First, simplify [tex]\( \frac{3}{3} \)[/tex]:
[tex]\[ \frac{3}{3} = 1 \][/tex]

Next, convert the mixed number [tex]\( 5\frac{3}{4} \)[/tex] into an improper fraction.
[tex]\[ 5\frac{3}{4} = 5 + \frac{3}{4} = \frac{20}{4} + \frac{3}{4} = \frac{23}{4} \][/tex]

Add the fractions:
[tex]\[ 1 + \frac{23}{4} = \frac{4}{4} + \frac{23}{4} = \frac{27}{4} \][/tex]

Converting this to a decimal:
[tex]\[ \frac{27}{4} = 6.75 \][/tex]

So, the result for this part is:
[tex]\[ 6.75 \][/tex]

### Part 6: [tex]\( x 3 \frac{4}{1} \)[/tex]
First, simplify [tex]\( 3 \frac{4}{1} \)[/tex]:
[tex]\[ 3 \frac{4}{1} = 3 \times 4 = 12 \][/tex]

Multiply by [tex]\( x \)[/tex]:
[tex]\[ x \times 12 \][/tex]

So, the result for this part is:
[tex]\[ x \times 12 \][/tex]

### Final Answer
Putting it all together, the detailed solution results in:
[tex]\[ (x \times \frac{1}{2}, 0.8333333333333334, 0.03125, 1.8333333333333333, 6.75, x \times 12) \][/tex]
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