`5cdot75-3/7xx15 3/4+2 2/35div1cdot44=?`

Options

A. `2/5`
B. `3/7`
C. `4/11`
D. `2/9`

Answer

To solve the expression \( 5 \cdot 75 - \frac{3}{7} \times 15 \frac{3}{4} + 2 \frac{2}{35} \div 1 \cdot 44 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 15 \frac{3}{4} \) to an improper fraction:
\[ 15 \frac{3}{4} = \frac{15 \times 4 + 3}{4} = \frac{60 + 3}{4} = \frac{63}{4} \]
2. Convert \( 2 \frac{2}{35} \) to an improper fraction:
\[ 2 \frac{2}{35} = \frac{2 \times 35 + 2}{35} = \frac{70 + 2}{35} = \frac{72}{35} \]

### Step 2: Rewrite the Expression
Now, rewrite the expression with the improper fractions:
\[ 5.75 - \frac{3}{7} \times \frac{63}{4} + \frac{72}{35} \div 1.44 \]

### Step 3: Convert Decimal to Fraction
Convert \( 5.75 \) and \( 1.44 \) to fractions:
1. \( 5.75 = \frac{575}{100} = \frac{23}{4} \)
2. \( 1.44 = \frac{144}{100} = \frac{36}{25} \)

### Step 4: Simplify the Expression
Now substitute these values back into the expression:
\[ \frac{23}{4} - \frac{3}{7} \times \frac{63}{4} + \frac{72}{35} \div \frac{36}{25} \]

### Step 5: Calculate Each Part
1. Calculate \( \frac{3}{7} \times \frac{63}{4} \):
\[ = \frac{3 \times 63}{7 \times 4} = \frac{189}{28} = \frac{27}{4} \]
2. Calculate \( \frac{72}{35} \div \frac{36}{25} \):
\[ = \frac{72}{35} \times \frac{25}{36} = \frac{72 \times 25}{35 \times 36} = \frac{1800}{1260} = \frac{30}{21} = \frac{10}{7} \]

### Step 6: Substitute Back and Combine
Now substitute these back into the expression:
\[ \frac{23}{4} - \frac{27}{4} + \frac{10}{7} \]
Combine the fractions:
\[ = \frac{23 - 27}{4} + \frac{10}{7} = \frac{-4}{4} + \frac{10}{7} = -1 + \frac{10}{7} \]

### Step 7: Convert to a Common Denominator
Convert \(-1\) to a fraction with a denominator of 7:
\[ -1 = -\frac{7}{7} \]
Now combine:
\[ -\frac{7}{7} + \frac{10}{7} = \frac{3}{7} \]

### Final Answer
Thus, the final answer is:
\[ \frac{3}{7} \]