To divide the fraction [tex]\(-\frac{5}{8}\)[/tex] by 12, we can follow these steps:
1. Rewrite the Division as Multiplication:
Dividing by 12 is the same as multiplying by its reciprocal. The reciprocal of 12 is [tex]\(\frac{1}{12}\)[/tex].
So, we rewrite:
[tex]\[
-\frac{5}{8} \div 12 = -\frac{5}{8} \times \frac{1}{12}
\][/tex]
2. Multiply the Fractions:
To multiply two fractions, we multiply the numerators together and the denominators together.
[tex]\[
\text{Numerator: } -5 \times 1 = -5
\][/tex]
[tex]\[
\text{Denominator: } 8 \times 12 = 96
\][/tex]
Thus, the product is:
[tex]\[
-\frac{5}{8} \times \frac{1}{12} = -\frac{5}{96}
\][/tex]
3. Simplify the Fraction:
We need to check if the fraction [tex]\(-\frac{5}{96}\)[/tex] can be simplified further.
The greatest common divisor (GCD) of 5 and 96 is 1 (since 5 is a prime number and does not divide 96 evenly).
Therefore, [tex]\(-\frac{5}{96}\)[/tex] is already in its simplest form.
The final answer is:
[tex]\[
-\frac{5}{96}
\][/tex]
