If A:B = 1:3 and B: C = 2:5. find A:C.

Answer

To solve the problem of finding the ratio A:C given the ratios A:B = 1:3 and B:C = 2:5, we can follow these steps:

### Step-by-Step Solution:

1. **Write the given ratios in fractional form:**
- From the ratio A:B = 1:3, we can express this as:
\[ \frac{A}{B} = \frac{1}{3} \]
- From the ratio B:C = 2:5, we can express this as:
\[ \frac{B}{C} = \frac{2}{5} \]

2. **Multiply the two ratios:**
- We need to find A:C, which can be derived by multiplying the two fractions:
\[ \frac{A}{B} \times \frac{B}{C} = \frac{1}{3} \times \frac{2}{5} \]

3. **Cancel out B:**
- When we multiply the fractions, the B in the numerator and denominator cancels out:
\[ \frac{A}{C} = \frac{1 \times 2}{3 \times 5} = \frac{2}{15} \]

4. **Express the result as a ratio:**
- The fraction \(\frac{2}{15}\) can be expressed as a ratio:
\[ A:C = 2:15 \]

### Final Answer:
Thus, the ratio A:C is \(2:15\).

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