To find the product of the fractions [tex]\( \frac{7}{8} \)[/tex] and [tex]\( \frac{3}{9} \)[/tex] and then reduce it to its lowest terms, follow these steps:
1. Multiply the numerators:
- Numerator of the first fraction: 7
- Numerator of the second fraction: 3
- Product of the numerators: [tex]\( 7 \times 3 = 21 \)[/tex]
2. Multiply the denominators:
- Denominator of the first fraction: 8
- Denominator of the second fraction: 9
- Product of the denominators: [tex]\( 8 \times 9 = 72 \)[/tex]
Therefore, the resulting fraction before reduction is [tex]\( \frac{21}{72} \)[/tex].
3. Reduce the fraction:
- Find the greatest common divisor (GCD) of 21 and 72. The GCD of 21 and 72 is 3.
- Divide both the numerator and the denominator by their GCD:
- Numerator: [tex]\( \frac{21}{3} = 7 \)[/tex]
- Denominator: [tex]\( \frac{72}{3} = 24 \)[/tex]
The reduced fraction is [tex]\( \frac{7}{24} \)[/tex].
So, [tex]\( \frac{7}{8} \times \frac{3}{9} \)[/tex] reduced to the lowest terms is [tex]\( \frac{7}{24} \)[/tex].
Hence, the correct choice from the options provided is [tex]\( \frac{7}{24} \)[/tex].
