If A:B=3:4 and B:C=12:13 find A:C.

Answer

To solve the problem of finding the ratio A:C given the ratios A:B = 3:4 and B:C = 12:13, we can follow these steps:

### Step 1: Write down the given ratios
We have:
- A:B = 3:4
- B:C = 12:13

### Step 2: Express A and C in terms of B
From the first ratio (A:B = 3:4), we can express A in terms of B:
- A = (3/4)B

From the second ratio (B:C = 12:13), we can express C in terms of B:
- C = (13/12)B

### Step 3: Substitute the value of B
Now, we need to find A:C. We can substitute the expressions we found for A and C:
- A:C = A/C = (3/4)B / (13/12)B

### Step 4: Simplify the ratio
When we divide (3/4)B by (13/12)B, the B cancels out:
- A:C = (3/4) / (13/12)

To divide fractions, we multiply by the reciprocal:
- A:C = (3/4) * (12/13)

### Step 5: Perform the multiplication
Now, multiply the numerators and the denominators:
- A:C = (3 * 12) / (4 * 13) = 36 / 52

### Step 6: Simplify the ratio
Now we simplify 36:52 by dividing both numbers by their greatest common divisor (GCD), which is 4:
- A:C = 36 ÷ 4 : 52 ÷ 4 = 9:13

### Final Answer
Thus, the ratio A:C is 9:13.

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