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Let's solve the questions from the worksheet one by one.

### Q1. **What should be added to \( \frac{38}{5} \) to get 18?**

We are looking for a number \( x \) such that:
\[
\frac{38}{5} + x = 18
\]
To solve for \( x \), subtract \( \frac{38}{5} \) from both sides:
\[
x = 18 - \frac{38}{5}
\]
First, convert 18 to a fraction with denominator 5:
\[
18 = \frac{90}{5}
\]
Now subtract:
\[
x = \frac{90}{5} - \frac{38}{5} = \frac{90 - 38}{5} = \frac{52}{5}
\]
Thus, \( x = \frac{52}{5} \).

---

### Q2. **Milk is sold at rupees \( \frac{67}{4} \) per litre. Find the cost of \( \frac{32}{5} \) litres of milk.**

We are asked to find the total cost for \( \frac{32}{5} \) litres of milk when the cost per litre is \( \frac{67}{4} \). The total cost is:
\[
\text{Total cost} = \frac{32}{5} \times \frac{67}{4}
\]
Multiply the numerators and the denominators:
\[
\frac{32 \times 67}{5 \times 4} = \frac{2144}{20}
\]
Simplify:
\[
\frac{2144}{20} = 107.2
\]
Thus, the cost of \( \frac{32}{5} \) litres of milk is ₹107.2.

---

### Q3. **By what number should \( \frac{56}{9} \) be multiplied to obtain \( \frac{3}{14} \)?**

We need to find a number \( x \) such that:
\[
\frac{56}{9} \times x = \frac{3}{14}
\]
To solve for \( x \), divide both sides by \( \frac{56}{9} \), which is the same as multiplying by the reciprocal \( \frac{9}{56} \):
\[
x = \frac{3}{14} \times \frac{9}{56} = \frac{3 \times 9}{14 \times 56} = \frac{27}{784}
\]
Thus, the number is \( \frac{27}{784} \).

---

### Q4. **List five rational numbers between \( -\frac{4}{5} \) and \( -\frac{2}{3} \).**

Convert both numbers to a common denominator for easy comparison. The LCM of 5 and 3 is 15.

- \( -\frac{4}{5} = -\frac{12}{15} \)
- \( -\frac{2}{3} = -\frac{10}{15} \)

We now look for five rational numbers between \( -\frac{12}{15} \) and \( -\frac{10}{15} \). Some possible choices are:
\[
-\frac{11}{15}, -\frac{121}{150}, -\frac{122}{150}, -\frac{111}{140}, -\frac{12.5}{15}
\]
This list includes numbers between \( -\frac{12}{15} \) and \( -\frac111--- not

Solve mathematical problems involving fractions, ratios, and simplifications.

This worksheet contains problems for Grade 7 students involving operations with fractions, finding rational numbers between given fractions, and simplifying complex expressions. Key concepts include fraction addition, multiplication, and rational number comparisons.

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