Find: a. `(10)/(21) xx (7)/(15)`

Options

A. `(5)/(9)`
B. `(4)/(9)`
C. `(2)/(9)`
D. `(1)/(9)`

Answer

To solve the problem \( \frac{10}{21} \times \frac{7}{15} \), we will follow these steps:

### Step 1: Write the fractions
We start with the two fractions:
\[ \frac{10}{21} \times \frac{7}{15} \]

### Step 2: Multiply the numerators and the denominators
We multiply the numerators together and the denominators together:
\[ \frac{10 \times 7}{21 \times 15} \]
Calculating the numerators:
\[ 10 \times 7 = 70 \]
Calculating the denominators:
\[ 21 \times 15 = 315 \]
So, we have:
\[ \frac{70}{315} \]

### Step 3: Simplify the fraction
Next, we simplify the fraction \( \frac{70}{315} \). To do this, we need to find the greatest common divisor (GCD) of 70 and 315.

#### Finding GCD:
- The factors of 70 are: \( 1, 2, 5, 7, 10, 14, 35, 70 \)
- The factors of 315 are: \( 1, 3, 5, 7, 9, 15, 21, 35, 63, 105, 315 \)

The greatest common factor is 35.

Now, we divide both the numerator and the denominator by their GCD:
\[ \frac{70 \div 35}{315 \div 35} = \frac{2}{9} \]

### Final Answer
Thus, the simplified result of \( \frac{10}{21} \times \frac{7}{15} \) is:
\[ \frac{2}{9} \]

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