If `A: B = 5 : 8` and `B : C = 18 : 25` find `A : C`

Options

A. `20 : 9`
B. `9 : 25`
C. `20 : 5`
D. `9 : 20`

Answer

To find the ratio \( A : C \) given the ratios \( A : B = 5 : 8 \) and \( B : C = 18 : 25 \), we can follow these steps:

### Step 1: Write the given ratios in fractional form
We can express the ratios as fractions:
- \( \frac{A}{B} = \frac{5}{8} \)
- \( \frac{B}{C} = \frac{18}{25} \)

### Step 2: Use the property of ratios
To find \( \frac{A}{C} \), we can multiply the two fractions:
\[ \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \]

### Step 3: Substitute the values
Substituting the values from the ratios:
\[ \frac{A}{C} = \frac{5}{8} \times \frac{18}{25} \]

### Step 4: Multiply the fractions
Now, we multiply the numerators and the denominators:
\[ \frac{A}{C} = \frac{5 \times 18}{8 \times 25} \]

### Step 5: Calculate the numerator and denominator
Calculating the numerator:
\[ 5 \times 18 = 90 \]
Calculating the denominator:
\[ 8 \times 25 = 200 \]
So, we have:
\[ \frac{A}{C} = \frac{90}{200} \]

### Step 6: Simplify the fraction
To simplify \( \frac{90}{200} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 10:
\[ \frac{90 \div 10}{200 \div 10} = \frac{9}{20} \]

### Step 7: Write the final ratio
Thus, the ratio \( A : C \) is:
\[ A : C = 9 : 20 \]