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