If a : b = 5 : 6 and b : c = 2 . 8 : 3.5 , find a : c

Answer

To solve the problem of finding the ratio \( a : c \) given \( a : b = 5 : 6 \) and \( b : c = 2.8 : 3.5 \), we can follow these steps:

### Step-by-Step Solution:

1. **Express the Ratios as Fractions:**
- From the ratio \( a : b = 5 : 6 \), we can write:
\[ \frac{a}{b} = \frac{5}{6} \]
- From the ratio \( b : c = 2.8 : 3.5 \), we can write:
\[ \frac{b}{c} = \frac{2.8}{3.5} \]

2. **Simplify the Fraction \( \frac{b}{c} \):**
- To simplify \( \frac{2.8}{3.5} \), we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{2.8 \times 10}{3.5 \times 10} = \frac{28}{35} \]
- Now, simplify \( \frac{28}{35} \):
\[ \frac{28 \div 7}{35 \div 7} = \frac{4}{5} \]
- Thus, we have:
\[ \frac{b}{c} = \frac{4}{5} \]

3. **Combine the Ratios:**
- We now have:
\[ \frac{a}{b} = \frac{5}{6} \quad \text{and} \quad \frac{b}{c} = \frac{4}{5} \]
- To find \( \frac{a}{c} \), we can multiply these two fractions:
\[ \frac{a}{c} = \frac{a}{b} \times \frac{b}{c} = \frac{5}{6} \times \frac{4}{5} \]

4. **Cancel out \( b \):**
- When we multiply, the \( b \) cancels out:
\[ \frac{a}{c} = \frac{5 \times 4}{6 \times 5} = \frac{20}{30} \]

5. **Simplify \( \frac{20}{30} \):**
- Now simplify \( \frac{20}{30} \):
\[ \frac{20 \div 10}{30 \div 10} = \frac{2}{3} \]

6. **Final Result:**
- Therefore, the ratio \( a : c \) is:
\[ a : c = 2 : 3 \]