If a:b = 4:5 and b:c = 2:3, then a:c=_____.

Options

A. `4:3`
B. `8:15`
C. `8:9`
D. `5:3`

Explanation

To solve the problem where \( a:b = 4:5 \) and \( b:c = 2:3 \), we need to find the ratio \( a:c \).

### Step-by-Step Solution:

1. **Express the Ratios in Fraction Form**:
- From the ratio \( a:b = 4:5 \), we can express it as:
\[ \frac{a}{b} = \frac{4}{5} \]
- From the ratio \( b:c = 2:3 \), we can express it as:
\[ \frac{b}{c} = \frac{2}{3} \]

2. **Express \( a \) in terms of \( b \)**:
- From \( \frac{a}{b} = \frac{4}{5} \), we can find \( a \) in terms of \( b \):
\[ a = \frac{4}{5}b \]

3. **Express \( c \) in terms of \( b \)**:
- From \( \frac{b}{c} = \frac{2}{3} \), we can find \( c \) in terms of \( b \):
\[ c = \frac{3}{2}b \]

4. **Substitute \( c \) in the ratio \( a:c \)**:
- Now we can express \( a:c \) using the values of \( a \) and \( c \):
\[ \frac{a}{c} = \frac{\frac{4}{5}b}{\frac{3}{2}b} \]

5. **Simplify the Ratio**:
- The \( b \) in the numerator and denominator cancels out:
\[ \frac{a}{c} = \frac{4/5}{3/2} = \frac{4}{5} \times \frac{2}{3} = \frac{8}{15} \]

6. **Final Ratio**:
- Therefore, the ratio \( a:c \) is:
\[ a:c = 8:15 \]

### Final Answer:
\[ a:c = 8:15 \]