To solve the problem of multiplying the fractions [tex]\( \frac{5}{6} \)[/tex] and [tex]\( \frac{34}{5} \)[/tex], follow these steps:
1. Multiply the numerators: Multiply the top numbers (numerators) of the fractions together.
[tex]\[
5 \times 34 = 170
\][/tex]
2. Multiply the denominators: Multiply the bottom numbers (denominators) of the fractions together.
[tex]\[
6 \times 5 = 30
\][/tex]
So, when you multiply the fractions, you get:
[tex]\[
\frac{5}{6} \times \frac{34}{5} = \frac{170}{30}
\][/tex]
3. Simplify the fraction: To simplify the fraction [tex]\( \frac{170}{30} \)[/tex], find the greatest common divisor (GCD) of the numerator (170) and the denominator (30).
The GCD of 170 and 30 is 10.
4. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{170 \div 10}{30 \div 10} = \frac{17}{3}
\][/tex]
Therefore, the simplest form of the result is:
[tex]\[
\frac{17}{3}
\][/tex]
So, if you multiply [tex]\( \frac{5}{6} \)[/tex] and [tex]\( \frac{34}{5} \)[/tex], the result in simplest form is [tex]\( \frac{17}{3} \)[/tex].
