To solve the problem of finding the product of the fractions [tex]\(\frac{12}{11}\)[/tex] and [tex]\(\frac{5}{8}\)[/tex], and writing it in lowest terms, follow these detailed steps:
1. Multiply the Numerators:
You need to multiply the numerators of the two fractions.
[tex]\[
12 \times 5 = 60
\][/tex]
2. Multiply the Denominators:
Then, multiply the denominators of the two fractions.
[tex]\[
11 \times 8 = 88
\][/tex]
So, the product of the two fractions is:
[tex]\[
\frac{12}{11} \cdot \frac{5}{8} = \frac{60}{88}
\][/tex]
3. Simplify the Fraction:
To simplify [tex]\(\frac{60}{88}\)[/tex], you need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 60 and 88 is 4.
4. Divide Both Numerator and Denominator by the GCD:
[tex]\[
\frac{60 \div 4}{88 \div 4} = \frac{15}{22}
\][/tex]
So, the fraction [tex]\(\frac{60}{88}\)[/tex] simplifies to [tex]\(\frac{15}{22}\)[/tex].
5. Conclusion:
Therefore, the product of [tex]\(\frac{12}{11}\)[/tex] and [tex]\(\frac{5}{8}\)[/tex], written in its lowest terms, is:
[tex]\[
\frac{12}{11} \cdot \frac{5}{8} = \frac{15}{22}
\][/tex]
Hence, [tex]\(\boxed{\frac{15}{22}}\)[/tex].
