If A:B = 3:5 and B: C = 8:11, find A.C.

Answer

To find the ratio A:C given the ratios A:B = 3:5 and B:C = 8:11, we can follow these steps:

### Step 1: Write down the given ratios
We have:
- A:B = 3:5
- B:C = 8:11

### Step 2: Express the ratios in fractional form
From the ratios, we can express them as:
- A/B = 3/5
- B/C = 8/11

### Step 3: Find A/C using the relationship of the ratios
To find A:C, we can use the relationship:
\[ A:C = A/B \times B/C \]

Substituting the values we have:
\[ A:C = \left(\frac{A}{B}\right) \times \left(\frac{B}{C}\right) = \left(\frac{3}{5}\right) \times \left(\frac{8}{11}\right) \]

### Step 4: Multiply the fractions
Now we multiply the fractions:
\[ A:C = \frac{3 \times 8}{5 \times 11} = \frac{24}{55} \]

### Step 5: Write the final ratio
Thus, the ratio A:C can be expressed as:
\[ A:C = 24:55 \]

### Final Answer
The ratio A:C is 24:55.

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