Are the following statements true?
7.5 litres : 15 litres = 5 kg : 10 kg

Answer

To determine if the statements \( 7.5 \text{ litres} : 15 \text{ litres} = 5 \text{ kg} : 10 \text{ kg} \) are true, we will compare the ratios on both sides step by step.

### Step 1: Write the Left-Hand Side (LHS) as a Fraction
The left-hand side of the statement is \( 7.5 \text{ litres} : 15 \text{ litres} \). We can express this ratio as a fraction:
\[ \text{LHS} = \frac{7.5 \text{ litres}}{15 \text{ litres}} \]

### Step 2: Simplify the LHS
Since both quantities are in litres, we can cancel the units:
\[ \text{LHS} = \frac{7.5}{15} \]
Now, we simplify \( \frac{7.5}{15} \):
\[ \text{LHS} = \frac{7.5 \div 7.5}{15 \div 7.5} = \frac{1}{2} \]

### Step 3: Write the Right-Hand Side (RHS) as a Fraction
The right-hand side of the statement is \( 5 \text{ kg} : 10 \text{ kg} \). We can express this ratio as a fraction:
\[ \text{RHS} = \frac{5 \text{ kg}}{10 \text{ kg}} \]

### Step 4: Simplify the RHS
Again, since both quantities are in kg, we can cancel the units:
\[ \text{RHS} = \frac{5}{10} \]
Now, we simplify \( \frac{5}{10} \):
\[ \text{RHS} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \]

### Step 5: Compare LHS and RHS
Now we compare the simplified values of LHS and RHS:
\[ \text{LHS} = \frac{1}{2} \quad \text{and} \quad \text{RHS} = \frac{1}{2} \]
Since both sides are equal, we conclude that:
\[ 7.5 \text{ litres} : 15 \text{ litres} = 5 \text{ kg} : 10 \text{ kg} \]

### Conclusion
The statement is **true**.

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