Which of the following statements are true ?
1.5 : 2.5 = 3.6 : 6

Answer

To determine whether the statement \( 1.5 : 2.5 = 3.6 : 6 \) is true, we will follow these steps:

### Step 1: Write the ratios as fractions
We can express the ratios as fractions:
\[ \frac{1.5}{2.5} \quad \text{and} \quad \frac{3.6}{6} \]

### Step 2: Remove the decimals
To simplify the fractions, we can remove the decimals. We can multiply both the numerator and the denominator of each fraction by 10 to eliminate the decimal points:
\[ \frac{1.5 \times 10}{2.5 \times 10} = \frac{15}{25} \quad \text{and} \quad \frac{3.6 \times 10}{6 \times 10} = \frac{36}{60} \]

### Step 3: Simplify the fractions
Now, we simplify both fractions:
- For \( \frac{15}{25} \):
- Divide both the numerator and the denominator by 5:
\[ \frac{15 \div 5}{25 \div 5} = \frac{3}{5} \]

- For \( \frac{36}{60} \):
- Divide both the numerator and the denominator by 12:
\[ \frac{36 \div 12}{60 \div 12} = \frac{3}{5} \]

### Step 4: Compare the simplified fractions
Now we have:
\[ \frac{1.5}{2.5} = \frac{3}{5} \quad \text{and} \quad \frac{3.6}{6} = \frac{3}{5} \]
Since both fractions are equal, we can conclude that:
\[ 1.5 : 2.5 = 3.6 : 6 \]

### Conclusion
Thus, the statement \( 1.5 : 2.5 = 3.6 : 6 \) is true.

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